Since the author of Amnesia kindly supplied the location of the plist…
~/Library/Group Containers/ group.com.apple.replayd/
I just went there and tweaked the ScreenCaptureApprovals.plist in BBEdit to look like this:
I won’t know if it works for a month or so, but it seems to be what everyone else is suggesting we do. 
Annoyingly, I also assume I’ll have to repeat this every time I give a new approval. Remember when Macs were easy to customize? 