I THINK I understand the challenge here. If you purchase the premium app, the app is going to know your Apple ID Your Apple ID owns the app. if for some reason you have a second Apple ID or a Google Play ID, it is going to look to collect $$$ from you for each license of the app. You might be able to talk to both Apple and Google and try and convince them that your IDs are for one person, but not sure how that will play out.
For my various iPhones and iPads, all different versions of operating systems, I am able to have the same file run on all my devices. I don't think that is your problem though. @Engineer-Joe has discussed that topic before.
John