Many old-tyme "drop thumb" banjoists play sitting down. Obviously there's no need for a strap then. Bonnie, a longgggg time before you decided to focus exclusively on that style, we talked (or I talked) about the many ways to play a five string banjo. For a while you seemed far more enthusiastic about a three finger semi-classical style. My approach is usually to go in the direction that folks decide on themselves, while trying to make sure they learn the basics of timing, good hand positions, chord sense....and (for me) most important...to be prepared for any playing eventualities.I prefer not to use a strap either,(I'm more relaxed that way) but sometimes you don't have the option of a chair. Not sure if you've seen Chris Coole in the subways yet, but I'll bet he plays standing up.
Some mandolinists (me) don't use a strap when standing, but many do.
Here's a suggestion. Check out Willie Nelson's strap configuration. He has a wool strap around his neck (only) and a little hook that goes under his guitar and hooks onto the soundhole. I'm sure that would work on banjo and might feel better.
If you really hate the idea of a strap, here's one more possibility (Carlos Montoya the Flamenco guitarist did this for many years). Carry your own chair (some kinda "fold-up" one) in the trunk of your car. You'll never get caught short that way.
Rick