Thanks, guys. I read that discussion just now... I have a "stock", unmodified vB4 running the latest non-beta version that I use to test things here:
https://lf3performance.com/
I just converted that over to SSL and it's got all the issues. Considering it's unmodified - I wonder if there's a certain type of server setting that's causing my problems. If some of you guys are simply installing the SSL certificate and updating the URLs in the Admin CP to get it working - then I'm surprised. I guess you're lucky...