gcrank1, your suggestion is excellent. Correct me if I'm wrong, but I believe the cavalry carbines were designed to be shot one handed while controlling the horse with the other. Hence the curved butt plate to fit the upper arm.
My horses were so gun shy when I first got them, you could fire a .22 and they'd be at the other end of the pasture looking for a way out. They soon realized the gun I carried created the "BOOM". If I went near them with a shotgun or rifle, they were gone. Today, thank God, I could lay a .45-70 between their ears and take a shot and still stay on their backs. Shooting off a horse is an art I still haven't mastered. If you're shooting at game or especially a predator, the horse sees it too, and he's squirming around to get a better look. It's a very unsteady, imperfect shooting rest and position. A person very skilled in reflexive instinct shooting could do well with it, but I'm afraid the indians (my wife's folks) would have had my scalp long ago.
Pete