Update -- found out why I can't find it. In addition to the tablet, I have the same app on a cheap, burner phone I keep on my desk for testing apps. No SIM card, so it has never been used as a phone, but it's an okay test bed.
When I fired up the app on the burner phone, it popped up a screen asking me to give it a 5-start rating. When I clicked okay, it took me into the Play Store ... where I discovered that the app is one of the ones I tested this afternoon, except that the current version is an update to what I have installed. And the updated version is just awful in comparison to the original.
So I know I can stop looking. Now I just have to figure out if I'm smart enough to use one of those .APK grabbers to download the app and install it on another device.