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I was thinking about a similar idea, while thinking about simultanous chess ideas:
This idea would be more suited for computer play.
On each turn, each player (or computer) make a list of all the moves he can do right know, then the player put this list in order from the movement he most want to do to the ones the he least want to do. If both players first move in this list, create a conflict, they flip a coin to choose what player will play their move first. 
After this move is played, the other player do the first move in his list that dont create a conflict with the movement the other player done. If he can't pick a movement from the list because the only movements that he is allowedto do that were not possible before, the player can choose what move he will do.

Conflict in this case, means both players moving their pieces to the same square, or one player making his own king be into check or mate after the move.
But other variants can be made that include more conflicts like, both players passing into the same square, one player going to a square a enemy piece was....


VARIANT:
A variant to this idea I proposed here, could be made to find a another way to fix the conflict.
Before each turn the player create a list of his movments and put them in order like in the other variant. But this list of movements would be different, the list would have all movements he would be able to do at this moment, and all the movements he would be able to do, if the enemy made a move right now and them he made his move.
Players flip a coin to decide who will move first. The one that win will get the first movement at his list (that include himself making a movement), after he make this movement, the other player get the first movement (that includes the enemy player moving making the move he did right know).

There is another variant but its even more complex.