Not being familiar with the lamp, I'm not sure he's in the breakover region -- the V-I curve that I'm familiar with for lamps like this has a large "constant voltage" region; if he's operating in that region then it should be easy to pull a constant current.
If he's getting out to the edge of that region, though, then life gets more difficult, or impossible: I think when you get close to the turn-off current there's some hysteresis in the V-I curve that's going to make it impossible to hold a steady current.