Jim (et al)
Agreed, 0-350mA at 1.5~2KV is quite a lot to handle. Under the circumstances you point out, given that negative screen current would not likely be much, series regulation with a sizable bleeder would seem the lesser of all evils.
But I can't help but think that if really stiff regulation is a priority perhaps a push-pull regulation scheme could be employed where neither supply nor shunt element need pass excess current unless required. As long as the unregulated supply voltage isn't too high dissipation could be held to a minimum.
As to the need of a REALLY stiff screen supply...
I've always considered the screen voltage primarily as a method of establishing the Mu of the tube, and accordingly, its saturation level, plate to grid leakage, etc. If allowed to fluctuate sufficiently this could be seen as a considerable source of non-linearity. The G2DAF amplifier design deliberately took advantage of just this trait.
However, I do not consider a less than stiff screen supply as a very significant cause of non-linear distortion.
Rather, I see improper bias a much more significant contributor to distortion products. I have always found that a higher than desirable bias usually yielded the most favorable outcomes for cleanliness, with or without really stiff screen voltages. Of such factors are compromises determined between efficiency and cleanliness.