I shoot right eyed and am right handed, so I carry my pouch on my right side where I can best get into it with my right hand. Back in the 70’s, I started putting my belt over the shoulder straps to hold the pouch firmly in place as Taylor mentioned and that works well especially when I’m running in some primitive matches. As I was taught in the 70’s, if you can’t run well with your gear or climb or descend the way you have it slung, you might ought to look at carrying it differently. I also carried my cartridge box the same way when I did a Confederate Marine impression. I can see how this could/would keep the pouch too low if I was normally on horseback, but I’m almost always on foot with a black powder gun.
I’ve tried the horn attached to the bag, but for me it works best for the horn to be on a separate strap and I carry it on my right side a bit above the pouch. I tried carrying my horn on my left side, but my left hand did not seem to have the coordination not to spill too much powder from the horn when filling the powder measure. Grin. I inherited “soft teeth” from my Mother’s side of the family and chipped a tooth once when pulling the horn plug out with my teeth, so I do it instead with my left hand.
There is no “right or wrong” way to carry your pouch and horn, it is all about what is best for you.
Gus