Well explained. I've been hoping Apple will resolve this for a while.
Currently a third party Screen Time restriction's app can be easily bypassed using the device Face ID in Settings. This means you can't impose restrictions on the user like you can with Apple's built in Screen Time functionality, where you can lock the restrictions behind a separate 'Screen Time Passcode'.
As you say, it would work well if you could set a different password (preferably supporting longer than 4 digit PINs or string passwords) that prevents you disabling the app's Screen Time access. And don't allow them to use the device Face ID to disable it. This password could be the existing Screen Time Passcode for consistency across the Screen Time settings.