Since it has been brought up...
As a Cavalry Reenactor, for some 30 years, I did sling a Sharps Carbine with an original snap hook and carbine thimble.
I also slung a Henry in Sling over may back from time to time.
Neither was comfortable, particularly at the canter, or gallop... The Henry could and occasionally did pop you in the back of your head.
The Sharps was heavy, and yanked on your shoulder, and on dismount and slung over the shoulder could and did smack you. You learned quickly to dismount without arching your back.
On the other hand, I had a M 1904 scabbard for my O3 in WW1 impression.
When it was rigged as regulation, it was under your leg and O4 stirrup strap making close contact leg grip uncomfortable.