I do not see the problem.
Your Deathmatch mode is point based and not last man standing, is it not? So you already have a rule system for giving out points without telling people on the loading screen that it is not last man standing. Or telling them the point rules.
And why would you need to create more mechanics? Or specifically tell them in the loading screen? Rolling over a bonus point to get a bonus point is not hard to grasp.
Do whatever game modes you think are fun to play in your game. If a host player opens the game, this is all idle thinking anyway. The host makes the decision which modifiers to the rules/mechnics are in place.
And if it is not a host that opens the game and you have some kind of lobby or matchmaking, restricting to few game modes is better, so players do not spread out and each plays a game mode alone, not finding other players.
