RE: Carrying a bow on horseback?
That sling looks fine to me. If I were in your shoes, I would use a fancy homemade sling made out of rope. My buddy uses an old lead rope. A thicker rope is nice bc/ it doesn't dig into your shoulder as much as a smaller diameter rope. A couple problems w/ a scabbard;
You have to be pretty agile when getting on your horse bc/ you have to lift your leg higher. It is very difficult to get on the right side of your horse if you want to. Your bow takes some licks. You can put it in a soft case and still get it into the scabbard if you want to. Brad