And *POOF!*, problem is solved! I went into the BIOS settings and it didn't allow exactly what you mentioned for options, Marv, but it allowed me to set it to start up at any specific TOD/DOW, so I set it for daily at midnight. There was also an AC restore mode, which I turned on. Apparently, this puts it right back to wherever it was when the power interruption occurred.
The nice thing about these power reset gadgets is that they give it a good 20-30 seconds of off time in order to perform a hard shut down.
As always, many thanks to you Marv and all who contributed. I can't imagine where I'd be in this industry without the immense knowledge of everyone here.