open your build.prop, create a backup and replace the following:
as long as you dont edit the fingerprint and build description, ...
if its the same rom but just an update, you should get away with just flashing it on top and wiping dalvik cache. as always BACKUP FIRST and then resore and wipe if its not working like it should.
dont go with MIUI yet as its had way less work don...
i am in the group who never touched amazon paid stuff. but you forget the advertising, movie rights and other such thing that make the fire an atractive platform to sell or advertise on. this probably makes up the difference