My 2 cents on three topics:
When a deed is eliminated, and the non-eliminated dudes on it go home unbooted, is this before or after the Sundown phase unboots them?
This is a huge question to me. Depending on how the rules answer this will dictate the extent to which the game incentivizes interaction - and specifically in three-player, cooperative chess shenanigans.
Why the strange double-circular-priority-assigned order? I would recommend sticking to simply passing left of the Winner. (But, see my next proposal).
Three player games are going to be complicated enough without creating this opportunity for the lovely intersection between misunderstanding and disagreement!
Dog in the Fight
(Proposed third alternative under Cheatin' and Interferrin')
If you want to make Shootout and Resolution plays, you have to have a dude in the fight. This includes plays that bring dudes into fight.
Again from an environment perspective, knowing that anyone from anywhere can snipe a Cheatin' Resolution into a fight they are not at all involved in will double or treble the pressure to not cheat. This is unfun to me because it undermines a fundamental dynamic in the game that holds the mechanics and incentives in balance.
My proposed mechanic creates a situation where there is at least the foreshadow of that additional pressure coming - sending an expendable dude third-party into a fight not because he will contribute to the poker but because he may contribute to the plays - also reinforces a fundamental axiom of the game that risk is never unhinged from reward.
By the way I love that these are finally happening! The option between The Quick and the Dead (Elimination) and Deadwood (Total Control) is especially awesome, and sets a precedent for third or fourth variants in the future. Well done team.
There is your positive and negative (constructive) feedback. Cheers.