Here's my idea on how to lessen it...
I don't think that you will ever manage to get rid of inflation. Even if you do people will find a way to do it again and you will have the same problem. The fix I propose is making players have less need for inflation. This could go into many different scenarios. Such as increasing the likely hood for legendary or certain cards. Another way might to decrease the amount that it costs to upgrade your card storage. For most people, they can get the first 1 bank upgrade pretty easy but then they turn to inflated cards after they see that it cost 4 to upgrade to a 200 card capvity. These things might help with the problem of people inflating so many cards, by lessening their need to inflate them.