Much thanks for that. It ultimately succeeded, but I don't know what it had to be so tortuous.
I gather the difference is that I had to start with the iPad off and iTunes not running. I tried this first with my older MacBook Pro, and it checked out the iPad in a different (much shorter) way than before, but told me it couldn't fix anything due to error 3194, which apparently meant my iTunes was out of date. I updated iTunes, and then even though I tried it starting with iPad and iTunes off, it handled it in the earlier way, insisting on spending about an hour to download something that ultimately did nothing (though I had to try it a number of times, since if I didn't watch it a message that my iPad needed to be restored would pop up, and if I didn't attend to it I'd get a message that the internet was interrupted so I'd need to start again. Shish!).
Finally I tried it again on my newer MacBook Pro and everything went smoothly and the iPad was restored in just a few minutes. But why does it have to have all the other complications? It's not what one normally expects from Apple.
I'm grateful for the help you two gave. Perhaps I should have been able to figure it out from earlier notes and FAQs, but my experience with the thing was such it was difficult to be sure I was actually on the right track.