You actually can transfer your Clash Royale (CR) from one Game Center to another, I've done it myself. What you need to do is go into CR, tap the gear icon, than tap help and support. You might see an option to "contact us." If you do not see that "contact us" button, follow these steps: Tap a support article, then look for an option asking If the article was helpful, then tap "no", then tap contact us (which appears after you tap no). You will be given a chat interface to talk to supercell.
In the chat explain to them exactly what your problem is, same as you have in your previous post.
This has to be done through supercell (CR developer) because they are the ones who linked their game to your Game Center account.
It might take a few days, as you have to prove that you are the account owner. It's worth the time though.
Trust me this works. I had the exact same problem as you with the annoying pop-ups.