Finished the first phase of moving two WordPress driven sites from one hosting service to another this morning. I was a bit wary, having read all the things that can go wrong, and I took a few wrong turns into dead ends. But I managed to back out and didn't screw up too badly on the first one. The screwing up I did accomplish was mainly the result of my impatience, doing things in quick succession when I should have given them time to settle down in between. But I learned my lessons, and this morning's transfer went much more smoothly. Scarily so, in fact.
There's plenty left to do, moving various ancillary things, all part of an ongoing effort to tidy up in general, but I don't foresee any more difficulties, touch wood.
And in case anyone cares, I couldn't have done it nearly as easily without the Duplicator plugin for WordPress, which truly is a life saver.