ROFLMAO!
4e's solution was ELEGANT, key every single heal to HS. Then they let up a bit on that later on, which could get problematic, but it never got completely crazy except for a couple edge case party builds (and Vampires are pretty wonky, but it kinda depends on the details of the party and combats).
So, my answer was, have a lot of non-combat SC-type stuff that sucked up resources and could produce drama in multiple ways. Then you could still have some basic fights, mainly just to provide the right atmosphere and suck up a few more resources. These would usually have some goals besides 'kill everything' to enhance interest, but in terms of fighting/damage its fine if the PCs just 'get up again', since they're unlikely to really be fighting to the death. Finally you get the really dramatic super action-packed fights where everything is a roller-coaster and I can insert some sort of 'special rules' (IE powers or terrain, whatever) to create the "and he goes down" sort of drama (falls are a cheap way to get this BTW). This is where nasty save ends effects can play a part, if used sparingly (and its best if there is a costly 'cure' available, way to create some tension). Heck, you can even throw in a '5 minutes' duration if you do that right, or even a permanent one.
Anyway, forcing the game to rely on hit points as THE way of doing this gets old fast, and every edition of D&D since thmake mid 90's has had a way around it.