Following a suggestion of our IT support, I was able to fix this. I haven't seen this before, so posting in case it's useful. Start a new scheduled (not instant) meeting with your personal meeting ID. That is, schedule a meeting, then you can start it immediately, and make sure the box to use your personal meeting ID is checked. This amazingly connects. Once that's done, end the meeting cleanly (the system is likely confused because some previous meeting was not ended cleanly or the system thought it wasn't). After you do this, instant meetings will work, at least they worked for me. Zoom tech support's idea of logging out of all devices (which you can do in your preferences) is a red herring. I thank our IT folks for this amazing suggestion.