Hi Chaos,
Your idea of usng a PWM system to control lamp current directly should certainly work, once the initial lamp discharge arc has been initiated. Running a lamp in "simmer mode" from a current source at low current is a very effective way to maintain a continuous lamp discharge at extremely low power.
This can most easily be done with a voltage source of several Kv dc, and a large high power series wire wound resistor. That could be quite independent of your PWM, and it may be easier to do it that way. The source impedance needs to be high enough to get a stable simmer action, otherwise getting it to start up may be problematic.
The lamp itself will have a very high negative resistance, and you need enough series impedance (positive resistance) to get a stable simmer current.
I doubt if the same inductor could be used for both trigger and pwm averaging, because the inductance/current requirements are quite different. The main PWM inductor will need to be air cored and maintain a reasonably constant inductance value over a very wide operating current range.
An independent series trigger transformer can then be placed between the main PWM inductor and the lamp. This need be only a couple of turns looped through several very high permeability toroids.
The idea here is that the trigger transformer will generate a very high voltage, with extremely fast rise-time, but from perhaps only a few, or tens of millijoules of trigger power. As soon as real lamp current begins to flow through the trigger transformer, the ferrite toroids massively saturate. The very high initial permeability and no gap will guarantee total saturation at perhaps a few hundred milliamps or less, and above that, the trigger transformer will have almost negligible inductance. Once the xenon lamp is conducting, the inductance of the trigger transformer effectively disappears from the circuit.
For your PWM inductor, consider a flat air cored pancake coil of rectangular section copper transformer wire. Several flat coils can be ganged in series for higher inductance.
A xenon lamp simmering with a single very long fine filament of plasma is a fascinating thing to see. The arc will twist and corkscrew from reaction to local magnetic fields. Rather like one of those decorative plasma ball displays.
I think you will find this is sure to be a fascinating and most memorable project.