There's really only two times I'm holding the frame in one hand for a rear wheel change: doing the little alignment tweak I describe above, and actually removing the wheel from the rear triangle. Any other time I mostly have the stays in both hands and use gravity (the ground), knees, a foot, or fingers and thumbs for the rest of it. (Front is different - stem in one fist, wheel in the other, pops right out.)
I'm sure bikes that are balanced differently respond better to different techniques ... and lighter makes everything easier/requires less finesse.
Re: resting the bike - mostly I just lay it on its side. Remember that nothing gets scuffed or even dirty unless you're applying pressure, which doesn't happen when a bike is resting rather than being manipulated. The only thing on a bike that might not take its own weight sideways would be a handlebar mirror - in that case, just lay it on the derailleur side. Again, if you lay it down gently, no problem. You'd lay it on its side at a rest stop with both wheels on ... this is no different.
Speed comes from what you put behind you. - Judi Ketteler