Would I would do is get a usb battery pack, it can/will be charged when power is on, will also keep it running on power loss/brownouts.
With the battery pack - the pi never looses power - just make sure you find one that will allow charging while the attached device is drawing power - amazon has a couple that I know of.
Just my 2 cents
I have put a lot of thought into this. Your assertions are pretty much where I am thinking.
1. Get a battery pack with pass through charging.
2. Pick a time that in no way could have a show still running (say 10:45 PM since the latest the gate closes is 10 PM on Friday and Saturday and the longest anyone would ever stay would be 30 minutes).
3. Set a shutdown sequence to run at 10:45PM. This will take the FPP offline for the evening.
Even if the battery should die, effectively powering down the FPP, there shouldn't
be any corruption.
4. Powering up the display the next day, usually 15-20 minutes before we open the gates, should bring the RPPs back online and ready to start at 5PM.
Thanks everyone for the ideas. I appreciate "group think" so much, especially when my brain is mush.