But I think it's asymmetrical to favor the attacker, because the king can only move one square at a time and space needs to be cleared behind it, while the attacking queens just need a clear line of sight.

Attacking the f pawn, the king side bishop, only requires 3 moves: move a pawn out of the way, move a queen into the field, take the pawn. On defense, you can't move the king backwards until the fourth move, and you'd be blocking yourself in so that moving the king backwards again will take at least another 3 moves. If you're moving backwards 2 rows in 7 moves, the attacking opponent can already check you a few times so that you might be forced to move forward or waste moves not productively moving backwards.

I need a playable board of this to really explore these ideas though.