Having only fairly recently come back to singing to an audience, I had a similar problem. As I'd never performed in public with the guitar I've been using until recently, I'd been playing strapless, sitting down. To play standing, I fixed a strap button in the neck heel, where most people have them and thought, bingo! But try as I may I could not get to hold the damn thing comfortably and eventualy went back to sitting down. I've recently bought a new guitar, which again only has one strap button. Being determined to get back on my feet, but being reluctant to take a drill to my new 'precious', I went back to the old fashioned method of attaching the top end of the strap via a cord to the top of the neck, and guess what? Every thing feels right. It may not look as tidy, but the guitar feels properly balanced. My hands are now just for playing the guitar, not holding or supporting it, and I seem to be able to move around the guitar, adjusting the hands to suit whatever action or position I need without discomfort. It even feels better with the strap when I'm sitting down to play!
It may not work for everyone, but it may be worth a try.