Here's my idea: we could take a cue from another famous roguelike, Nethack, and have two different "neverending" modes: Explore Mode and Wizard Mode.
Features of Explore mode:
-Unlocked by dying on HMP or lower 10 times.
-When your health drops to 0% or lower, you are asked if you really want to die. If you say "n," your health is restored to 100%.
-Your score is not recorded in the rankings.
-Can be played in ITYTD or HNTR levels.
-No red stairs are generated.
-Items and enemies are generated as normal in levels 1-24.
-Level 25 has no Cyberdemon. Instead there is a weaker boss fight. Maybe an ArchVile and two Barons?
-You cannot do any challenges in explore mode.
Features of Wizard mode:
-Unlocked by defeating the game on HMP (maybe UV?) or better. In other words, you have to be good at the game but not UNGODLY good.
-When your health drops to 0% or lower, you are asked if you really want to die. If you say "n," your health is restored to 100% (same as Explore Mode).
-Your score is not recorded in the rankings (same as Explore Mode).
-Can be played at any difficulty level except Nightmare.
-Pressing "w" (or maybe a function key like F12 would be better) brings up the "wizard mode" menu. In that menu, you can give yourself any item, powerup, or trait. Including uniques. You can also warp to any level of the game, including special levels. You can also turn challenges on and off.
-Invincibility can be toggled on and off. Maybe by typing iddqd?
-You can create any enemy, in any quantity that you want.
-If you beat the Cyberdemon, it would be recorded but with a funny message like "1 soldier defeated the Cyberdemon using trickery."
So what do you think? Maybe it needs some tweaking on the details, but I think this would work very well.