Okay, major overhaul time!

*player->health (formerly the "HUD" health) is now to be known as player->rings, and now acts as the player's actual ring count
*player->mo->health (formerly rings + 1) is now always 1 when alive, regardless of ring count; if player with rings is damaged, this is untouched

Damage in normal SP/Coop gameplay has been tested and still works fine; still a lot of mess to clear up though

Tag damaging probably is broken now, I'll fix this later