I wasn't able to devote uninterrupted time to troubleshooting so it took a while, but my issue is now resolved (at least temporarily...

).
I ran MemTest 86+ with all my memory installed in the original configuration. After 8 passes it showed lots of errors. I then started testing each stick in each slot, one at a time. I only got errors in one configuration - the first stick in the first slot. That stick didn't produce errors in any other slot, and none of the other sticks produced errors in that slot. I ran a minimum of 8 passes on each stick/slot combination.
I then installed all the memory, making sure not to put the one stick in the one slot that produced errors. I then ran 12 passes of MemTest86+ and received no error warnings.
I'm still not sure whether the stick is to blame or the slot, but at least for now I have a stable system again.
Thanks for the help and advice, I truly appreciate it.
-Mike