Allthough wouldn't your name and address be tied to the cards anyway(Last time i checked my billing address is tied to all my physical and virtual creditcards), so it should still be possible to tie the purchases to the individual.
Yeah, that's true.
However, I think you need to give up on limiting number of accounts. What's to stop me from having my relatives or friends buying me additional accounts?
If you design the game where having multiple accounts gives the player a major advantage, the players that actually manage to get multiple accounts (and they will!) will certainly break the integrity.