Looks like BatMon is not designed to do what I need (and you have to pay after the trial period), and UPS-Assistant is not compatible with my UPS (I already tried it :-( )
Using BLAT, I wrote a CMD script that sends me an e-mail when it is run, logging the time in the e-mail itself (a modified version of the one that runs when each of my PCs boots up).
I found that my UPS software does log a Windows even (in the Applications log), when the UPS switches from AC to battery and back.
Windows 7 allows you to create a scheduled task to be triggered by a certain event ID.
I set up tasks to run my "power is out" and "power is back on" scripts based on those events, and it seems to work (verified this morning when we lost power).
My "Home Automation and Other Stuff" server is on the UPS, as are my router, monitor (turned off when not being used), and KVM. The only problem is that if power is out for more than a few minutes, then my Verizon FiOS system drops the Internet and TV services, to conserve battery power for the phone system. I don't think it recovers fast enough for the "power is back on" e-mail to go out, but since all of my non UPS-ed PCs e-mail me when they boot up, I'd have a pretty good idea.
Perhaps I'll modify the "power is back on" script with a delay before it sends the message, to give time for my router to reconnect.