I was able to finally get Google Photos to back everything up. It's not a perfect solution, but it does seem to work for now.
Uninstall / Reinstall.
I just completely uninstalled the app, then immediately reinstalled it from the Google Play store. One of the first things it asked about in its "first-time setup" procedure was whether or not I wanted it to ...
You can use adb backup. You can specify the package name for backup a single app.
adb backup [-f <file>] [-apk|-noapk] [-obb|-noobb] [-shared|-noshared] [-all] [-system|nosystem] [-keyvalue|-nokeyvalue] [<packages...>]
adb restore <file>
Note: some apps won't allow adb backup. even if adb backup is allowed, cache is not included.