The current ffa rules and mechanics don't take relative seating into account, nor how many players are left.
We could build a wall only knights can jump over to prevent sides from clashing early.
We could change the starting position, scramble the pieces in a way that no two players are natural allies.
We could morph the position onto a 3player chess board when 1st player is out (except we can't..)
We could let the middle player move twice every third turn.
Being a game of points, you need points to win, and not necessarily a winning position. You don't een have to be alive. This provides a lot of flexibility. We could change how points are earned.
With the current board layout, starting position, and rules on standings and points, the name of the game is: who is the stronger team of opposites. it's pretty close to a teams game, because the odds to win when you become the middle player 3-way are so slim. You can't afford to lose your opposite.
0 points for kings? fine. But it seems it won't change anything in this regard.
Are we sure winner takes all will change this?