Derp! When I copied-and-pasted the Apache SSL settings from one of my other sites to this site, a lengthy string listing allowable encryption settings got cut off. This kept the site from coming up on all but the latest versions of most web browsers.
This has been fixed. The only browser anybody’s even somewhat likely to be using that still won’t work is Internet Explorer on Windows XP, and that will never work because it doesn’t support SNI. (SNI support is needed to access HTTPS websites that share a webserver with other HTTPS websites.) IE should work on newer versions of Windows (and Edge works on Windows 10). Safari and Chrome will work wherever they’re supported. As long as it’s not too old and crusty, it’ll probably work. (Hell, Safari on my old iPad that’s stuck at iOS 5.something works!)