Yep, a great thread.
My saddle gun, in fact my only gun for 40 years, was my Fajen thumbhole stocked 270 Winny w/a 24" bbl and Leupold VX-II 3-9.
I made my own scabbard which left the butt stock stick out. I hung it on the horn vertically. Only bad thing was the thumbhole to the butt plate was above the top of the horn.
Two instances readily come to mind. One was being bucked off and tracking the horse for 20 minutes hoping I had a whole rifle when I found her.
Second was when the two other fellas decided to push a canyon on foot an head for camp. I was chosen to take the horses. I was instructed to ride the bay, not my horse, as she hesitated crossing water. Yep, at the first trickle of a creek she hesitated. My horse, with the rifle sticking up, and the other horse blasted by and away they went.
I went back to camp fully expecting to be greeted by the two nags. Didn't happen. A little after dark, hours later, here they come trotting home. Yep, my rifle was intact.
I had it all worked out when I was going to be afoot with a goat packing the rifle. With me now on a donk w/the goats packing I'll have to work something out. Don't know what but I bet its unique.
Also, as with Jeff, the use will be mainly for woofs. My 28" plus a short brake in 270 Am @ 12 pounds will suit me just fine.