I think you probably answered you own questions with your first comment.......you have never used a sling before. Size doesn't matter that much unless you carry it across your chest and back. Just slinging it on the shoulder, that sling should be fine. I am larger than you and it works for me. Personally, I prefer the "Claw" slings as they bite a little better to the clothing and don't slip off as easily. I assume you carry your rifle barrel up on your shoulder? Try it barrel down. I think this position always feels more comfortable.
But you don't have to "break it" in.......more like you have to break "you in"! You will get used to it.