Ok, it looks like this functionality in sqwebmail 3.6.2 is broken. (is anyone else able to change passwords in 3.6.2?)
I installed 3.6.0 with the same configure options and it works fine. I'd post this message on the sqwebmail list, but it'll just be ignored like the rest of my messages. Hopefully someone working on that project will see this and take a look at it.