I say also keep a record of deaths/kills for kdr's
This was a part of the entire idea, to be honest.
though i wouldn't do one life. i'd say something more like first team to Xty points, and on top of that first to 2 wins. its a little less immediately punishing but still keeps things easy-to-understand
After experimenting various games, I found that a GameMode based on one-life will force players to create decisions quickly, prove their skill, and put pressure on every move.
The GameMode itself isn't very complicated and is a pretty barebones team-deathmatch with a handful of weapons to go around. At the spawn of each map, a player is given a long range weapon, a short range weapon, and a melee weapon that can almost instantly kill a player if they don't react. By this I mean a knife, machete, chainsaw, whatever it may be, you still have to sneak up on someone who could easily kill you in two shots.
The weapons wouldn't be anything stupid and has been thought of a long time ago. A player would be given an Old School Sniper Rifle, Double Barrel Shotgun, Chainsaw, and several Pills. The sniper rifle would serve as a long range weapon, the shotgun would protect in close quarters, while the chainsaw would serve as a trophy collecter. The pills of course, would heal you.
The GameMode would have several maps on rotation, after ten rounds, the team first to win five rounds would be victorious and the map would change based on the losers decision. On rotation, the teams would scramble unless the GameMode is in tournament mode.
Tournament mode would be organized teams, with brackets and play times. Team with the most map wins, wins. The map number would be odd.
Competitive mode would offer easy to join, easy to leave, fun and bragful gameplay. The maps would constantly remain on cycle.
I'm not sure what else to add, but this sounds about right. I'm still thinking about third person ...
Edit: In tournament mode, anyone can watch, but the players can only interact with each other. Viewers could only spectate and talk in viewer chat -- this would bring some real heat in. Imagine a server clocked at 56 players where only 10 are playing and it's a serious finale!
I could host; my internet's good enough that I no longer see complaints from most players, even with a large number of players. (This was really convenient when I hosted for /v/ a little while ago)

As for the idea, it seems like a lot of fun; I can't say I have a lot by way of ideas, but I would like to help if at all possible.
You would constantly need to host, I'm sure it would become bothersome.