I'd like to see the player automatically get to go first for false god fights. If you went first in a fight, you drew one less card, to balance the advantage of going first. With the false god's drawing ability, not drawing the 8th card at the beginning isn't really a penalty for it. So if a false god goes first, it gets the inherent advantage in doing that, plus doesn't suffer the penalty imposed on whoever goes first.
If yall decide this is another one of those "false god fights are supposed to be unfair" along with the 200 hps, 2 card drawing ability and juiced mark, fwm, but I do think it's something to look at and consider.