I was actually thinking they should add a multi-level PVE mode and came to suggest it before seeing your post! Honestly, this place needs a new mode to shake things up. The balance of power tourney is neat, but otherwise pretty much the same 'ol.
Your idea of using all your heroes might be impractical at this point. It’d be nice if they tried one for 3 team members, with escalating enemy difficulties. Figuring out if boosts worked between rounds might be a problem.
The ability to cash out or lose rewards at the end would be interesting too. They could also have some sort of boost that lets you keep your rewards up to the last level you beat if you end up losing or retreating.
I really can’t see an auto-recover unless it’s temporary healing or shields.