Followup: I finally found how to solve the problem.
I bought the universal license as in-App purchase, but for some reason was not directly forwarded to the registration screen. As I downloaded all three Apps simultaniously, I later tried from a different application to restore my purchase, which (obviously) did not work. So what you need to do is:
Check the purchase confirmation you received from Apple for the application you used to purchase the license, and restore your purchase from exactly this application. This should redirect you to the registration form for the Affinity account. Register it there and afterwards start the other applications and activate them using your Affinity account.
Please note: The universal only works over an affinity account.