PvP matchups should be on a hidden cycle.

Make matchups cyclic so you fight everyone, but make the cycle determined at the start of the game and don't show the cycle to the players. It gets rid of most of the RNG, and eliminates optimizing for certain matchups (except for knowing who's left to fight at the end of the cycle if you were paying attention). Change the cycle after 7 PvP rounds. You could potentially face the same person back-to-back at the cycle change (like a snake draft if it RNGs that way), but you'd always be on pace to fight everyone the same number of times.