Thank you, funkydunk! That was a helpful post that you passed along from the tech support guys ... I didn't realize I was having an Apache crash when this was happening.
Just for grins, I tried turning off the storage of session data in MySQL ... since my non-SSL store and the site WITH the SSL cert that we're piggybacking on happen to be on the same server, everything is working without MySQL session storage.
So -- the problem is resolved for me, so long as the HTTP host and HTTPS host are on the same box. I can imagine this will continue to be a problem for other people who have HTTPS service on a seperate machine.
Thanks again for your post, funky! You saved me a lot of headache!
-Clay