Hmmm, yeah something like that. Problem may be, that the first side that charges will suffer a lot, as their medic wouldn't be able to get to all of the wounded. Also, if both sides had incompetent medics, the numbers could dwindle on both sides, leading to a boring stalemate...
In the direction of your idea, maybe the maximum number of soldiers for each side should be based on the difference between wounded recovered by each side? So if they've brought back 10, and you've brought back 5, they'd have a max of, say, 40, and you'd have 35. The battles would still last for a while, but you'd have an even greater impact on the outcome. It might even be apparent now... though luck would still dictate success to some extent.
As far as the medic respawning goes, you're only going to have one life -- the cause of death in the high score list depends on it, for instance. Having more lives would make all of that less personal. However, what I should probably do is make the german medic respawn less often. So if their medic is killed, they have to wait quite a while to get a new one, and you can clean up in the mean time. If you die, the allies will get a new medic too, you just won't be there to see it. He he he. Or even worse, maybe I'll have the new one run on to the bottom of the screen and get to work while the screen fades out... yes, grim continuity...
Speaking of which, if the boundary of your open set is continuously differentiable, you can approximate a sobolev function by C-infinity fcns up to the boundary, rather than only getting interior regularity.