Here was an idea someone had, but the links are all broken because of photobucket.
http://www.ft86club.com/forums/showthread.php?t=26259
What he did was buy a Lexus key fob like below, and transfer the internals of the current fob, which fit right in under the new buttons.
https://www.amazon.com/KeylessOption...=lexus+key+fob
Then get the blank cut to match the physical key you have.
This way you avoid reprogramming, which I don't believe anyone has actually done with the '15 keys for a 13' car.