My mistake. I looked back at my first post to this thread and I unchecked "Enable Power Nap" and "Wake for network access" as a troubleshooting step, which didn't work. I'm guessing that nothing will work at this point but it doesn't hurt to try certain suggestions so I am currently running with the following settings.
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I am using a Mac Mini with an LG TV connected via HDMI so after 15 minutes the computer goes into low-power mode (wakes up with a keystroke or mouse movement). In this case, I don't believe the "Prevent.." option applies. Anyway, it hasn't crashed in almost 2 days but I don't expect that to last. If it does crash again I will just shut it down overnight or for long absences until this is fixed.