I also have a tough time with the rear brake cable on my LHT. Closing up the front brake is easy. Not sure what it is about the rear brake that makes it such a pain.

I started inverting the bike for rear wheel removal after almost dropping the whole thing on multiple occasions. I figured that a scuff on the saddle or handlebar (both easily prevented with a saddle cover, jacket, plastic bag, etc.) was better than dropping the bike and getting stranded with a bent derailleur or broken rear fender. I also hated laying the bike down on its side while the rear wheel was off, because that exposed even more components to the sidewalk and usually resulted in a mis-aligned front fender. I'm curious: what do you non-inverters do with the bike while you fix the flat?

To invert the bike easily, I lean over the frame, grab the seat stay with my right hand, the front rack or fork with my left hand, and brace the frame a little with my body so it doesn't flip over too fast. I don't have much upper body strength, so it takes a little muscle for me, but it's easier and quicker than holding the frame with one hand and fiddling with the wheel, chain and derailleur with the other hand ever was. I find myself using many fewer four-letter words this way.