You can work in the States on a J-1 visa as a flying instructor for a couple of years after training. There are only two ways into the country long term. First is through a H-1 visa which requires a degree and a job offer. Unless you are an experienced JAA FI then at the moment a H-1 is unlikely. The only other way in is through marriage. I've met a few foreign pilots who have got involved in marriages of convenience (MOC) to obtain the green card to stay in the country. One guy was being blackmailed for more money from his "wife." The other bloke worked for a regional turboprop outfit and then flew regional jets. In the end he decided to come "home" to our side of the pond. If that doesn't put you off then there are websites that act as introduction agencies for MOC's. If you do get caught out you may well end up having your collar felt by the cops or thrown out of the country.
Judging by people I know in aviation there are jobs in the States with most of the regionals hiring briskly. Of course there are plenty of people applying for them. Even with a green card, cutting through the security check red tape would be tough for a Brit. If you are "lucky" you can fly RHS in a turboprop for £10,000 per annum for the next three or four years.
I can sympathise with your position. It took me three years and two bouts of LASIK surgery to get my JAA Class 1 medical. Why not ask in the medical forum if there is a way round your problems?