"Is the 1.10% difference from AMEX's 15% to NFCU 13.9% going to make a difference?"
If you keep paying $400 a month until the $16000 is paid off, it will take 56 months at 15% and 54 months at 13.9%. You didn't mention what the fees were for transferring (beside the $10 for the one card) so possibly the 54 months will be higher.
Since there is a good chance Amex will either close your account or bring your limit down to a few hundred dollars if you transfer the balance away the new card won't really help with utilization. With that and the 1% difference in mind, I personally would leave everything where it is and guard the new card with my life Then when you find a job, throw everything you can at the cards and pay them off sooner..
I would assume you can't get a personal loan without a job but if you can, that would be the better option if the rate is better.