If you want to make 16x3 decks to cheat so that you can punish them, you need to employ heavy bullet reduction effects and reduce them into draws. If you do that, they rarely have a choice to avoid it.
Law Dogs are great for doing this, starting Wendy and running SIYE, Pinned Down, and Pistol Whips and a lot of anti-cheating.
The point is not so much to win all games, but to affect your meta enough where one cannot rely on a 16x3 structure to always carry them to victory. Until your local meta learns this lesson the hard way, it may be too difficult to use other shootout structures effectively.
Another easy method to win them - never shoot. Just avoid as much shootouts as you can and build deck with this idea in mind. Use such cards as Make smart choice, Pistol Whip, Paralisys Mark, moving cards(mustang, shadow walk), pack blood curse, rumours for finishing turn. Winning every lowball helps to build so much dudes that they cannot kidnep them all. And soon they spread all their dudes and lose to rumours turn.
I play a lot of 3/16 or 16/14/14 Law Dogs and anything that forces me to cheat is just awful. Coachwhip can be a huge problem, even in lowball as Booting key shooters like Wendy effectively ruins my turn. Pistol Whip is a big pain as well, and Unprepared is sometimes enough to ruin a day. SIYE, is gross as well, as it almost always forces a cheating hand.
A defensive Slide deck with good clubs can push me out long enough to overwhelm, especially if I don’t get my own deeds. Avoid shootouts at all costs unless you can force and punish the cheat.
Typically in my experience a 16x3 deck trades capability for probability. Non 16x3 decks trade for the opposite. But since most decks are structurally similar in terms of what the best and worst hands they can make are all your doing by running a 16x3 deck is giving yourself a higher CHANCE of drawing what you want.
But who plays poker without a shotgun in their lap?
In all honesty the best way to beat chance is to combat it with guaranteed happenings. So if I say run a 14-14-12-8 structure and those 8 cards are say shotguns and point blanks, I now have potential to disregard the shootout all together which skews the way my opponent has to play.