I was reading into this last night, thinking i bet it could be done and its so much simpler than talking to some clueless EA chat advisor for hours begging them to unban/unlink your account and them saying they are powerless.

1. Basically, obviously your gamertag is linked to the email and it is the email that is banned. I assume we all know that at least. Thats why unlinking your account would work, but ea aren't allowing that anymore.

2. All you have to do is change your gamertag, Yes it really is as simple as that.
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Read the post by II Sanzee II
There it shows that when you change your gamertag it does not update on the EA system automatically.

3. So what now? Well after you have changed your gamertag you must go onto your harddrive and delete everything associated with an EA game, I recommend using this list and checking every game on your harddrive to see it is on there.
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I only say that because there are some games that are EA that i didn't even know about. Also do the same with an external usb devices you may have.

4. Once you are sure all EA game data is removed from harddrive, this includes full games you have installed You must now download an EA demo, NBA2K12 for example, there once you have downloaded that you can play it and upon loading it you will be asked to apply an email to this account, there you just put in an email that isnt in use on ea.com (Make a new email if you have to)

5. You are now unbanned. In answer to a question i think i will get, YES you will have lost all your Ultimate team, and all other things associated with fifa and other ea games. You may also need to buy a new online pass, but i think it would be worth it if you want your account back that badly.

Hope this helps many people, i hope you don't go back to 127 modded pro afterwards though as you all know that you can actually get banned, play the game legit.
Once you have done this feel free to thank me, plus rep, whatever.