Here's my idea for a 5-8-Q Horse chess deck out of the stables. It isn't shootout-focused, as is evident by the horses and actions chosen, but it's still got an alright 3 value structure. It's untested and also not optimised for top level tournament play before anybody points out how it'll fail against a lot of popular current decktypes. I can definitely see the actions changing around a bit after playtesting it when I inevitably find myself sorely lacking Cheatin' Resolutions while on the receiving end of a barrage of aggro jobs.
The general plan here is to make use of your mobility to annoy your opponent while building up your dudes and deeds before taking advantage of your mobility in the "chess phase" to pick on isolated dudes and call them out (so like most of my Morgan decks it's slide-lite that's not scared of a fight). The home's react will be useful for cycling cards after playing a movement ability and repositioning another dude, doing a spot of shopping or calling someone out where their friends can't help them. This last point is why Clear Out! is in the deck, because unless your opponent is watching your discard pile like a hawk they won't be expecting your dude to fly across town and call them out in one move when all your Mustangs are booted, also I've never seen anyone playing the card before and I wanted to use it :)