kstan

I see... Well, I am my own hosting provider (although I don't really know what I'm doing), and I did in fact have ModSecurity installed. It seemed like a difficult and risky task to just turn it off altogether, so instead I experimented with turning certain features off, and lo and behold, turning off "Backend Compression" did the trick!
Thank you for saving me!

I just want to report that the problem has finally been resolved. In the end converting the database to utf8mb4 did the trick. I can't find it now, but I think someone at some point asked me why I hadn't done that. I replied that I intended to, but I wanted the other problem resolved first before messing with converting the database. Nowhere that I saw was utf8mb4 listed as a requirement to upgrade, but nonetheless, that's what solved it.
Thank you to everybody who tried to help. Much appreciated!

I deleted a cookie and voila, I was back in business. It then asked me to add a line to my constants.php, and after doing that, the rest worked smoothly.
Thank you for your help.