I also just learned a couple weeks ago that apps can finally opt-into having Apple's Family Sharing feature work for in-app purchases, which I did for Synthesia immediately.
I am trying to unlock Synthesia on my wife's iPad, which is the only one that supports my Roland FP-30X's bluetooth MIDI connection. We have family sharing set up. I get "There was a problem purchasing or restoring. (Leave this screen and return to try again.)" when I click the "Restore Purchase" button.
Hmm, it sounds like you're doing everything right. And this surprises me more because I haven't heard anyone ask about this one (one way or the other) in what feels like years now, so I would have assumed it was doing what it was supposed to.
My only advice would be to double-check in which "direction" you have the family sharing stuff set up. (I haven't personally used it, so I don't know if that's even a real concept. Is there one "primary" account that all of the sub-accounts need to be under? Or are there peer/mutual accounts that can share in both directions?)
If nothing works, the workarounds are either to use an unlock key from the website (if you've got one) or to very temporarily log into the other iPad with the account that made the purchase (just long enough to unlock the app).
That would be disconcerting if something changed and this broke though.