Many ballasts have PFC i.e. boost converter in them. Many are rated "100..240V" AC. I'd expect them to handle big voltage range..

What about some cell ballancer along the lines of :

 - long string of diodes in series

 - Parallel to each diode is a cell + a mosfet that connects/disconnects this cell

 - When the cell goes below wanted voltage the transistor is shut off and only the path through the diode remains

Of course anything you build is cooler then what you can buy, and your only limited to your imagination not corporate shareholder interests, now about the gas engine, you can use pretty much anything to power a small HID light like a 35 or 70 watt HPS, a half decent chain saw is able to run about 1 kW, a weed whacker (well my cheap $50 Home Depot special is 1 HP) is able to do about 600 watts and leaf blower the handheld type can do about 350 to 450 watts, and for simplicity you would want to normally use a 12 volt alternator from a car or truck, you can use other motors but then you need to get into regulation and RPM control of the gas engine and you can get a one wire alternator at most junk yards and they will be complete with a pulley and mounting holes for bolts, and because it's DC it doesn't really care about the engine speed so long as they rotate fast enough. Now yes you can weld it right to the engine output shaft, if you get it perfectly centered and it has the required bearings, or it will vibrate to death in short order, even if your a pro at welding I would strongly advise against doing that, it's much easier to either to use a belt or a coupler (like a  spider coupler) to go from the engine to the alternator, and both make servicing it later so much simpler then having to get out the cutting torch or saw.

About the fuel, most small two stoke engine or reed engines in chainsaws, weed whackers, and leaf blowers, use mixed fuel, so you need to add oil to the gas, in a ratio of about 32 parts gas to 1 part oil some are 40:1 and even 50:1 check the fuel cap but on the positive side they don't care which position you operate them in, yes you can use a chainsaw upside down, with a four stroke normally they don't like that and don't last long..

But don't overlook used lawnmowers (normally they are 4 stoke engines) they are great for a small DC generator and at a yard sale I've seen go for $5, if they pull easy, normally the carb is gummed up and needs to be cleaned or you just need to add some fuel that is not 20 years old (those are the two most common problems, really fuel today doesn't keep long) About fuel usage a gallon of gas will give you about 4 kWh of power, at a good guess..

If you go with an automotive alternator you will need a small 12 volt source to start the power generation something like a 7 Amp hour battery SLA works great and also helps to filter the output and provide enough power to start a larger loads, or larger to make it though refueling periods when you need to shut it down,  and then if you go with a solid state ballast you can use a cheap inverter, if you go magnetic you should use a pure sine wave inverter (look for a used APC smart UPS they are cheap, but you have to mod the alternator to 24 volts, not to hard or get a larger truck one already set to 24 volts, and they have enough room for small batteries and you might even be able to remote mount the ballast inside the box)

Here's a good website about building one from a lawnmower, with a nice write up and pictures  https://theepicenter.com/blog/generator-lawn-mower-vertical/

And while the guy in the instructable uses plywood for the frame, if you have access to a welder and some scrap metal I would build a small metal frame and or look for a busted pressure washer so you can use the wheeled cart to mount it on, yes it's still lighter then a huge lead acid battery, but wheels will make it so much easier when your tired and as you get older..    

About the lawnmower idea vertical shafts are pretty easy to deal with, I almost think they are easier then a horizontal shaft engine, you just remove the blade, attach a weight to act like a harmonic balancer (large metal disk that weighs about the same as the blade did) and add a pulley to the output shaft, they make them to bolt on, and cut a hole in the top of the mower deck and drop in an alternator, find the right length belt and you have a 12 volt 1kW generator, and about the speed control, yes its important like Medved pointed out, engine speed  will affect the output frequency of a mains voltage type alternator, which is why I suggested using an automotive style alternator they output DC so the engine speed doesn't matter, then use an  inverter which will do the rest of the work to control the frequency and voltage output. If you go with a smaller light like 70 watt HPS with the correct pulley sizes you can run the engine at pretty much idle so they are quieter and consume less fuel and then speed them up if you go with a high wattage lamp, also on the plus side you can run small power tools, charge batteries, boost a car with ease, run a plug in cooler, power a TV or a radio, or run a sump pump at the same time as you run your light/s..   

And about Medved's post on the Li-ions, that was to address Ash's post on using a long sting of batteries in series to output a much higher voltage, while you can do this, and they are light and very nice when set up and working correctly, it's nothing short of a designers nightmare to get it right and last a long time..

About the automotive Alternator, If you go with a single wire unit they will have a built in regulator, some might have two wires, one wire is power and one is to power the idiot light on the dash telling you there is a problem, if they have more wires odds are good they need an external alternator hit the junk yard and see what cars they have and use google it will tell you what style the alternator is and the amperage, normally I just hit older GM trucks they are simple to remove and you can get replacement bearings and brushes with a single / dual wire output and they are pretty common so if you need to replace one you can find one and then you don't have to change anything on the engine or drill new holes..   

About the operating costs, yes gas is expensive and grid supplied power is cheaper, but the setup costs with batteries and replacement batteries adds up, and for a small load like you looking at and long run times a used as engine and used alternator with an inverter is cheaper to build, has more versatility but it will cost more per hour to run, I could power a 1000W HPS right now for 12 hours and it would cost me about $6 USD in fuel vs about $1.50 in power, but I can refuel in 1 minute vs 12 hours of recharging a battery, and if there is a major power outage I can find fuel and not worry about a dead battery, and I can also put some of that regular unleaded in a coleman lantern without fear (in fact it's all I run in them) so I always have light.. 

Then i can just replace the resistor to higher value, it will take a second more to start...

With SMPS is there need in such discharge circuit ? The SMPS alone still works (or atleast tries to) downto <50V, how long would it take do deplete a capacitor even when it is without load on the SMPS output ?

Do you have access to a welder? The flywheel (weight) could be something as simple as a small disc brake rotor, they are round heavy and smooth, and for the most part pretty well balanced, and junk yards sell them cheap.. And repairing a small lawnmower is not that hard, honestly most I've seen start up with ease once you drain the old fuel, clean the crud out of the tank, clean the spark plug and refuel them with fresh gas, people like to leave gas in them over winter, if you do your asking for trouble especially if the gas has ethanol added to it (most gas does) when spring comes around they don't start. This causes people to throw them away because like you they think they can't fix them,and taking them to a shop is just as much as buying a new one from walmart, when all you need is a spark, fuel and air that's all that it takes. 

Then the odd one needs the carb bowl removed and clean the gum out with a little bit of carb cleaner, normally a single screw in the bottom of the bowl, or the odd small gasket like the one around the carb bowl to stop air leaks, or worst I've had to replace the flapper valve (takes about 10 min and coffee change) really they are pretty simple machines, to tell if it works just give them a pull see if feels like a good lawnmower (hit up a home depot and give a few new ones a pull to learn how it should feel if you don't have one at home, and if you do, whatever you do, DON'T use that one because your parents will be less then impressed, even if it works.)

In the junk yard finds I would recommend pulling the spark plug and use a flashlight to see if every thing looks clean on what ever you find, and pull the rope slowly and make sure every thing is moving (watch your eyes, sometimes stuff sprays out of them, normally I will give it a good pull away from my face then go looking in it), and depending on the junk yard if you find it with fuel in it try and start it up, the worst is you leave it behind if it doesn't start... 

About the alternator, look at all the trucks first before you pull anything, and remember where the cleanest newest ones are and go after those ones first, I've found ones that look brand new before and aim for the highest amperage ones (really use google or rockauto's website to see the AMP ratings) and take a good chunk of the wiring harness with you, it's nice heavy copper and will be made with the correct size connectors/plugs and normally it goes right to the battery so it's easy to pull out as they are only a few feet long, and check the headlight sometimes you get lucky and they have aftermarket HID kits in them, and if you see any older Cadillacs like from the 2000;s check the front grill, some contain a thermal image camera (really) and they have analog outputs so you can plug them right in a simple tv, and then you can see how hot things like ballasts or light fixtures are running, also great for trouble shooting breaker panels...   

thoughts on this inverter?
http://www.ebay.com/itm/Chicago-Electric-2000-4000-Watt-Power-Inverter-/322588145415

I did search up the inverters you mentioned lodge but was confused by the results (different ratings, wattages, shapes and sizes ect), I do like the one in the previous link because it is small, has indicators and is not flashy or weirdly designed like some of the other things out there:
https://www.ebay.com/p/Energizer-EN2000-2000-Watt-Power-Inverter/1908010962?iid=271246619761
Gross...
just... yeah no.
 (I don't like building with things that aren't roughly box shaped), it just makes things harder to mount/fit for one and two it is hard to deal with looking at something that looks like a giant Tylenol with legs and blue eyes or some animal that obviously ate too much for its own good, IDK think of a better description if you must, but those  are what i can think of lol...

I like my stuff utilitarian, and simple, this is why i hate alot of modern cars, well that and they prettymuch all started to look the same to me after 2014 and not in a way (I'd) consider attractive, also why i dont care for alot of modern electronics, like those new smart TV things... they lack alot of the connections that are useful to me, and they have a weird form so they take up more space than their counterparts (or past counterparts IDK if they killed off normal TV's) I also hate cloud storage and societies idea of Modern/Futuristic... ahhhhh. some accuse me of not liking change. maybe thats the case, i cant tell to be honest

Anyway, sorry for the rant try to focus more on what i typed before all that, that was the original question... then my mind kinda trailed off  

Lawnmower engine flywheel: I think it is not needed to use explicit flywheel there, as the mass of a larger pulley would beenough.
The problem is, in anycase you need to have thing perfectly balanced, otherwise it will either fall apart, or at least prematurely wear the shaft bearing (or its housing; that would mean effectively killing the engine). Andheavier the thing, more difficult is to balance it well (although heavier flywheel makes mainly the starts easier).