If you can find a company that thinks it can sponsor your H1-B Green Card to be an aircraft engineer the sad fact of the matter is that they're probably both mistaken and completely clueless about immigration law and what's involved. But don't let envy one tell you it's impossible either.
As I see it you have basically two options
- Diversity Lottery Program
I know of an Irish guy that got his this way and as far as I know Irish are still eligible. Check though because it's based on your country of birth.
- Set up a business
If you invest a substantial amount in a business in the US you can apply for an E2 visa valid for 5 years. This would also allow you to work for other outfits on a contract basis. Beware though because since most are totally naive about the law they may think you're trying to pull the wool when you say you can contract but not be an employee.
Either of these cases should satisfy the FAA requirements you're talking about. Whatever you do don't try and do it on your own. I went the business route and it worked well for me. If you need a recommendation for a lawyer, PM me and I'll introduce you.
I'm married to a US Citizen now so I can't comment on renewals since five grand in fees later the problem goes away.