I wanted to update that I monkeyed around with the sleep settings, and so far it seems to have helped with random shutdowns. I tried "never" and the battery heated up and the system froze and wouldn't turn off. I let the battery run out, and then all was fine. I now have the sleep and screen settings at "1-hour" and the network setting at "never." Battery doesn't last as long, and I may try reducing the 1-hour setting, but hasn't randomly shutdown since. Fingers crossed.
Bro, this method you tried (runing out of battery once), how is it so far?