need to use a different game center account on new iPad

years ago i set up an iPad with my main apple id for iTunes, iCloud, App store, but with a different Game Center ID for game play on the same device.

I am about to retire that iPad, and have purchased a new one. I am signed in with my main Apple ID as above, but when I try to use the different Game Center log in, it doesn't work.

I've tried the 'forgot apple id' and 'forgot password' routine, and am told my email address doesn't exist in the system. Yet I have confirmation emails from Apple to the contrary.

So, how do I get in to use the game center account, yet have a different apple Id for everything else?

thanks