Thanks for all the replies. (And hi Mark!)

To start, I never realized the cable tension changed on an IGH depending on what gear you had it in. I've never paid attention to what gear it was in when I took the wheel off. Maybe that's part of the "fussiness" I'm claiming to find. Also, I also look at this as the "work bike", so I usually want to have my trailer hitch on the axle, and for the winter I have a set of Reelights that I like to run, which also go on the axle, so trying to get all those things tightened onto the axle and also get the chain tension right, well, it's kind of a pain when you only have two hands, especially if I'm changing a flat on the side of the road in 30-degree F weather. (Thankfully, that doesn't actually happen too often, but theoretically it could. But my garage is none too warm in the Maine winter either, even with a space heater.)

What seems to happen is that I'll get it right before I start tightening, then when I tighten it seems the chain is a different tension than when I started tightening. I've learned to tighten alternating sides a little bit at a time, instead of each all at once, but it still sometimes takes me a few tries. I think I'm just a slow learner mechanically.

Finally, the hybrid I'm looking to replace is getting pretty old and the dropouts could be getting corroded or worn, so I'm sure that doesn't help.

By the way, in terms of the shifter cable issue, after several times taking the cable off and not being able to get it back on (I told you I'm not mechanically inclined), I did figure out how to change the tube without taking the cable off, but of course that still involves at least taking the wheel out of the dropouts.

Anyway, thanks for the education. The Axle Release product in particular looks like a good compromise. Sure, it only saves you having to carry a wrench, but I might consider them worth the convenience for the reasonable price.