You won't believe this... It's BACK!!!
I didn't do anything, oddly enough. Last night, I ended up reading till about 4 a.m. Tossed and turned, thinking about the calls I'd need to make. Then about half an hour ago, I thought I might as well try again. Just once. To my astonishment, Safari worked.
Why? I have absolutely no idea. But it's an enormous relief. It can, and probably will, happen again if I don't do something. I plan to call Verizon, explain the situation, and ask them to straighten out the problem with overlapping channels. At least now I know for sure that it has to do with Verizon, rather than Apple.
So it all seems more manageable now. Thank you again for all your help. It really made a difference, and helped me understand what was going on. Though I hope never again to see that diagnostic stuff.
Thanks to everyone else who helped, too.