In fact, the only one I so far haven't been able to persuade to run under Win2K is Hexen II, which is a shame because it's a nice game.

Perhaps one of the recent code-ports of the Doom source code will run the Hexen 2 wadfiles? Such as Doom Legacy?

I haven't run the original code for any of the Doom variants in a long time, I've been running Legacy or Zdoom. I seem to recall reading in their dox that they supported the Hexen games too.