Hi, Mika!
I had set up the SSL exactly as described in the FAQ. I also set up Cloudflare exactly as described in the FAQ, but never updated the IP address of my server after DreamHost moved it a few weeks back. Once I removed the Cloudflare line from my wp-config file, everything has started working perfectly. (I wasn’t using Cloudflare anymore anyway, so it didn’t make a difference at all one way or the other.)
tl;dr: Oops, m’bad! ??
Thanks for all your help!
