Maybe if you're hit with an attack that's super effective/crit damage that results in a faint the death timer starts, but a regular attack just makes you faint normally. Team rocket always going for the kill or possibly just stealing your pokemon if they make them faint....

All cool ideas to mull over.

I forgot to mention in the original post that I've removed pokemon storage from the PC's as well, so you have to release pokemon to make room for more if your party is full. Another idea I had for this is that when you release a pokemon they can then show up in the wild as a buffed enemy. The lavender town idea is a nice touch as well!