This might be a controversial take, but I kind of wish they do not split the player base into different matchmaking pools. Make "cross-play off" a soft preference instead (for all platforms, including PC), and add a preference for only playing with same input type (mnk / controller).
These preferences should only be inputs to the matchmaking system, so the matchmaking will consider your choices, but can not guarantee them. This way all players will exist in the same matchmaking pool, and can potentially be matched after a certain threshold (for example after 2-5 minutes) if the system can not find enough players based on your preferences. This will ensure a healthy player base for the game in the long run.
Then focus on balancing the inputs instead. The current aim-assist system in BF6 is a good start, but the lowered recoil for controllers should be removed.