Ok so I have this 600W HPS lamp that I used to use as a flood light in my backyard, up until the ballast insulation broke down and went dead-short to the casing.

So I had an idea. Could I possibly use a 500W halogen flood light as a ballast, paired up with an igniter to run the 600W HPS bulb? Being 100W short I'm guessing it wouldn't warm up as quick, but would it work?? Or 2 250W halogens in series with a centre tap?

Thanks for any feedback on it

The problem is not that much of "what wattage" it needs, but "if ever" it will work...
I'm afraid a resistive ballast won't be able to keep the arc going, it has too long zero current gap (around the current zero crossing), so the ionization decays too much there. Plus just after that the voltage is rather imited, so will yield quite long and high reignition overshoots. So long and so high, the lamp will too likely not reignite at all.
But you may try.
The lamp needs 6A current with just about 150Vrms across the incandescent, so something between 1200 till 1700W (depends, how much the filament resistance differs)

Way better approach would be to "assemble" the ballast from multiple lower power chokes connected in parallel to yield the required current (e.g. 2x "250W HPS" in parallel lead 5.9A, so pretty close; the rest may come from some fluorescent choke or so). On the plus side, it will allow some dimming...

Instead of all the alternatives-why not get a replacement ballast?This would be the easiest and most economical approach.When I have purchased new ballasts-they are not that expensive.

Nobody sells 600W ballasts around where I live, let alone any decent lighting equipment.  And plus, from a hobbyists point of view I want to know and see what would happen and wether it's possible

 (in the name of research and development! )

@Medved thanks for the info on that, I'll give it a try and see what happens

The various plant light suppliers sell 600W HPS bulbs,fixtures and possibly replacement ballasts.You could probably order one from one of those companies "online".Those would be good to try.

Middendorps may have one, other than that, it'll be an online job

600 watt HPS is mainly only used as horticultural lighting.  Many of the ballasts also tend to be electronic.  You maybe able to find one through a horticultural supplier, either in store or online, or part out an HPS grow light for it's ballast.  I understand the hobbiest interest in building/fixing it yourself, but in this case, it maybe better off in the long run to find a standard HPS outdoor light, either 400 or 750 watt.  Would likely be better suited to the conditions, and should it need repair in the future, parts will be easier to find.  You will also end up with a more reliable core and coil magnetic ballast.

A couple of other issues with using a resistive bulb for an HPS ballast are voltage drop and the ignitor itself.  Higher wattage HPS lamps run on 100+ volts, and when wired in series with a resistive ballast on 120 volts, the end voltage would be too low for the lamp.  Such higher voltage HID lamps require an autotransformer style ballast to operate on 120v.  As for the ignitor, most ignitors are of the semiparallel type, where the ignitor only starts the pulse, but uses the windings of the ballast as an "ignition coil" to build up the required voltage to strike the lamp.

Ah OK. Yeah that might be the way to go in terms of a new ballast, although using resistive ballasts over here I'd be running them on a 240V supply, would I still have voltage drop issues?