I like my Hiscox Pro II tenor case but I HATED the shoulder strap. I bought another from Amazon but it wasn't much better. Then I was buying a carryon case from Tom Bihn - I've been using their excellent messenger bags for years - and I noticed their "Absolute Strap" and thought I'd try it. Not only does the strap "say put" on the shoulder, I'll swear it makes the case 5 lbs. lighter. Highly recommended. My adjustment was to take up virtually all the slack on one end of the strap (the "narrow end" of the case) and let the other end out all the way.
https://www.tombihn.com/products/shoulder-straps?variant=16664457159
https://www.tombihn.com/products/shoulder-straps?variant=16664457159