You said that Amex will not convert your card, which one do you have? You can transfer regular Amex Membership rewards points to your TB account. Since it is a ratio of 250 to 1 you would need 17,000 points to transfer to get a reward ticket. Just transferring the points does not extend the expiration, you would have to transfer enough to get a ticket. (Which also expires in a year) Also, you can have somebody else apply for the Amex and put in your TB account number. This would of course requite the cooperation of a friend or relative with better credit.
-Dave