I don't understand the reference to the "Southwest" position of rifle scabbards located on the right side of the saddle, with the rifle butt facing the rear! If the "near side" butt forward is the "Northwest" carry, wouldn't the former be a "Southeast" carry? It has been many years since I went horseback hunting, packing a rifle in a scabbard...on the "Southeast" side carry. I kept the rifle from falling out of the scabbard going uphill by the simple expedient of having a "half-flap" that buttoned to the scabbard body and for a bolt action rifle, the flap had a hole in it that fit over the bolt handle. Never lost a rifle that way. I could dismount, unbuttoning the flap, grasping the rifle by the stock wrist, and pulling it free just before I swung my leg over the horse's rump. I could also reach across the horse and pull the rifle while dismounted.
The U.S. Cavalry used the sling swivel with the carbine supported by the trooper's shoulder. To keep the carbine from flopping around, the muzzle was shoved through a leather socket attached to the saddle rigging. The problem with this was that in the event the trooper was thrown from his horse, the carbine could keep him hung up! A sergeant came up with an open-front socket made of leather-covered spring steel that would allow the carbine to pull loose in such an event!