It is also possible that the Amex Blue Cash card is a valid downgrade option. So rather than cancel the Jetblue, you could downgrade to the no annual fee Blue Cash and have access to the Amex offers that way, as well as keeping the credit line open.

Also, for the OP, it's important to understand exactly how credit scores are calculated. If you close a card, it usually remains on your credit report for up to 10 years, so you don't lose age immediately. This thread may be helpful, as it touches on several of the levers in FICO:

http://www.flyertalk.com/forum/credi...ilization.html