The only stories I've heard of people working here post training, as instructors, were unpaid (a requirement of their F1 visas) and there was a strict limit to the amount of time they could work.
That's strange. Why would anyone work for free on F1? Sorting on-campus (and yes, FTO would be on-campus for aviation training that includes flying somewhere with affiliated school) student work authorisation - up to 20hr/wk during term, 35 summer hols. Even off-campus work is still possible, but should be backed by financial hardship yada yada and specifically authorised. Casual PT jobs are to pay bills/rent/drinks. Even if we talk about OPT post-F1, why should it be free work? Yes, some paperwork required, but..
As for JAA planks instructing, NAC advertise for unrestricted JAA instructors who'd also do ME training, FAA certs desired, think 200h dual given or something in that line. As JAA school, they'd sort H1 for you. You can look hard on PPRuNe and you'd find some past threads/posts.
So, definitely not a starter job, even for experienced past PPL pilot, since the dual given requirement, obviously.
As for the F1 route, if you don't have FAA CPL/IR/CFI/CFII, you won't get much credit for aviation associate degrees with some community colleges. Although these could be 2 years, USD 10k+ for tuition (total, if RPL OK) and living cost proof of funding etc. Why would FW pilot go through that only to instruct in the USA? Although FAA CPL wouldn't be too much hassle and you should get some credit towards CFI/I if you'd have done JAA FI.
As for H2 visa, it's for seasonal, mostly agricultural or hospitality/catering jobs. It doesn't come free either.