I've been running 4 magnetic Advance ballast (71A5005-500DP) with a 3000 K Philips Par 30 CMH for ages they don't seem to have any issues at all, but they get nice long run times and not much switching (12 on 12 off.) to keep a bunch of outdoor plants alive all winter long.

I have acquired some 35/39W CMH lamps, some in 4000K and some in 3000K. I've noticed the Philips 4000K have an indication on the box to use only with electronic ballasts. The 3000K do not have that mention. Now, I have some GE 4000K that do not mention anything about ballast type. I've always used electronic ballasts, but I'm tempted in obtaining a magnetic ballast for a new MH project. I would probably like some 4000K lamp, but what harm would there be in using the Philips ones ?

I have some Philips 4000K in higher wattages, one of which came with a magnetically ballasted 100W flood light, and no problems.

I would recommend you get an electronic ballast. you can (and I have) used a magnetic ballast on these lamps, but as their electrodes are physically smaller than they are in quartz lamps, extended use on magnetic ballasts can cause the lamp to wear prematurely.

There are two main behavior differences between electronic vs magnetic:
- The electronic can easily incorporate some advanced supervisory functions, which are to quite significant extend prevent EOL lamp explosions.
- The electronic is able to keep the delivered power rather independent on the actual arc voltage, so "break" the positive thermal feedback (hotter lamp->more fill evaporates->higher pressure->higher arc voltage->higher power->hotter lamp), so ensure way better thermal stability of the system. The consequence could be the longer lamp life, but the main motivation here is better color consistency and so therefore color quality (important over large group of even different age lamps in the installation). Some lamps are "rated for electronic only" just because without the thermal stabilization feature they are not able to meet the advertised color performance over the whole life.

It will physically run on a magnetic ballast, but for metal halide lamps of 35W and smaller this really hammers the electrodes and shortens lamp life quite drastically.  The problem is that the electrodes of 35W metal halide are very tiny, and if you run them on 50/60Hz they cool down too much between each half-cycle of the mains (although at 60Hz the problem is notably reduced vs 50Hz).  The arc then re-ignites from an electrode that is too cool, and does a similar kind of damage to the electrode as when the lamp is started from cold.  This means increased sputtering of tungsten that blackens the arc tube wall, reducing light output.  It also raises the wall temperature leading to reduced life from halide corrosion reactions.

Is it possible to overdrive the lamp just enough to avoid this problem without running into something else ?

Is it possible to overdrive the lamp just enough to avoid this problem without running into something else ?

Then just after the peak current the electrode would be way too hot.
The main problem here is, the thermal inertia of the electrodes is too low to ensure stable temperature: During the peak it overheats and after the valley it cools down too much, all with the single lamp on a single ballast just running in front of you.
The only remedy here is either to even out the heat generation during the supply current cycle (the square wave means constant heating with very small gaps), increase the frequency (so to reduce the temperature "ripple", so the difference between the hottest and coldest state) and/or to make the electrode heavier (so to have higher inertia)
The first two are the way, how the electronic ballast solves the problem, the last would mean the electrode would have larger surface as well, so need higher power to keep it on the required temperature. That means you would have at least higher electrode losses, but that means lower efficacy, so something these designs want to address as their first objective.
You may look at it as the electrode mass serving as a kind of filter, the only thing that makes the difference between the hottest and coldest temperature during the cycle low enough to fit between the minimum emission level on the cold side and the excessive evaporation temperature on the hot end.

What if the power is left 50Hz sine, but the peak of the sine is "PWM'd off" with a simple semiconductor switch ? (without rectification to DC and generation of new signal like proper eHID ballast) ?

What if the power is left 50Hz sine, but the peak of the sine is "PWM'd off" with a simple semiconductor switch ? (without rectification to DC and generation of new signal like proper eHID ballast) ?

You would need a fast, low ohmic bidirectional switch capable to shunt the current.
Plus to maintain the average power, you would need to increase the coil current, so the arc peak current (i.e. high crest factor), what would increase the cathode emission loading, so the sputter. So you would gain something on the lower temperature ripple, but loose somethig on the crest factor.
So a result would be pretty complex contraption, with all the EMC stuff not much less complex than the real decent electronic ballast and providing only moderate improvement.