Took me way too long, but I've finally managed to get SSL working on the ol' site (the problem, for people who care, will follow).
The home page now has that nice little lock that lets you know the site's secure, as do pages such as login, registration and commenting. You may still run across pages with broken-lock icons, but that's because I've been hard coding links that start with http:// since I was knee-high to a grasshopper. One good MySQL command'll fix that, but, to be honest, Sunday night isn't the best time to do that for somebody whose grasp of SQL commands is shaky, even if I did just back up the whole database.
As for why it took me so long, when I got an SSL certificate a few months back, I could never get it to work, no matter how much fiddling I did with .htaccess. Sometimes, I'd wind up with some weird "too many redirects" error. A lot of the times, nothing at all would happen.
And yet, the other sites I host on the same platform worked fine as soon as I turned on their certificates. The problem, it turned out, is that I'm using CloudFlare for image caching (and secondarily for protection against various Bad Things). The fault wasn't CloudFlare's, though - it was mine, because I never flipped the switch to let them know I now had an SSL certificate on the server. Once I did that, whammo, SSL started working within a couple hours.