From my experience, not all bikes are alike! Give your bike a good shove and make sure it’s one of the asymptotically stable ones before you try your next “no-hander!”
I think it has something to do with the angle of the front fork… but regardless, my most recent bike won’t even stand up at the bike rack – it’s always the one that falls over when the handlebars get turned even the slightest bit. So it’s not just about the gyroscopic effect, it’s also about the effect of precession on the turning mechanism.
I’ll be in Boston tomorrow through Saturday evening. Are you still up there?