jaa usa
I'd be carefull of your interpretation of US immigration laws. Going over to the USA to instruct without any remuneration is not going to be viewed in the same light as you might think. Since 9/11, the USA has cracked right down on people coming in and out of the country and when it comes to flying either you are training or you are working as far as the authorities are concerned (both of which required a visa in the passport).
Most FTOs requiring JAA instructors may be reluctant to let you work even if you are not getting paid since the authorities will come down on them as much as you if found out. If you get deported, then you could be faced with a 10 year ban in your passport!!