Comments/Ratings for a Single Item

I have to wonder whether this game would benefit from adapting Yonin's ruleset (specifically, when a player is checked, it's their turn next).  If you did this, then I guess whoever checkmated either player first would win, since in free-for-all Yonin you have to be in control of three out of four armies to win.

Alternatively, instead of just passing the turn to a checked player - if a player is checked "out of order" simply reverse the turn order.  But that might be too confusing in the long run.

Also, I haven't ever played any games that use this other particular option, but I like it in principle: without using either of the above rules, what if you won if the player to your left (the one after you) was checkmated?

You seem to be under the assumption that this game is won by checkmate. It is not. The object is to possess all three kings, and even if you lose a king, you still have the chance to get it back. So your suggestion would not really fix anything. Also, you have to consider that the "checked" player's other opponent may have incentive to not let the "checking" player get the king, and it would be a bad move to expose another player's king to capture by your other opponent. Besides no need for this rule change, it would make the game harder to program, and it would not make sense if a move left multiple kings in "check". I have put "check" in quotation marks, because there is no check in this game.