Yeah it is annoying. EA and BT really do come across as hugely ignorant and self-centred. So many people have this issue and no-one has even offered to help. My experience online with gaming since switching to BT has been horrendous. I regret changing from Sky.
Out of interest, are you getting to do this while still in contract and without any cancellation fees?
You're lucky they are not charging you for the remainder of your Infinity contract. If you don't get an improved gaming experience I suppose you could always "upgrade" to Infinity again if you wanted.
I thought that you were rubbish when you posted you won 6 out of 40 but didn't want to say anything. Keep us posted how you get on.