In the MP game I’m working on, I use GameModes to set up rules for the current game and all stats are stored in my game state for that game mode. Example: A game of Team Death Match uses my TDM game mode to set the rules and the TDMState to track all the information such as points, score, players, teams, win conditions, etc. iirc, the game mode is only accessed by the server but the clients can access information from the game state.
So you should be able to save all your information in the game state and use it between levels as long as the levels use the same mode and state.