SBAB
If you don't have too much money to burn then why on earth are you trying for an instructors rating in the states. Before you can work as an instructor, you will need to pass your FAA CPL probably on both a multi and single. Also pass an IR and the complete the CFI and CFII courses. Plus you need to go through a whole world of ball ache in gaining the right visa to work.
Chances are it will cost much more than a JAA FI ticket. Plenty of work going for a keen instructor who doesn't mind which end of the country he/she works.
Good Luck.