Thanks so much for responding, Jeff. I found the source of the problem and also the solution. I was testing about a dozen different login plugins, including theme-my-login, and at some point I stupidly deleted the TML login page.
The fix was simple once I realized what had happened. I removed and completely deleted TML. Then I went into the WP database options table, found two records created by TML and deleted them. I also deleted other records from plugins I had tested and rejected. Then I reinstalled and reactivated TML and everything now works perfectly.
I must say that after all that testing, no other plugin came close to giving me the features I needed. And a bonus: your tutorial on modifying the registration form to collect my users’ first and last names saved the day for me.
Thanks again for a great plugin.