You should be able to get a regional job very quickly with no problem.
The only thing holding you back from the best majors would be be PIC time (which you could get quickly at a regional) and a four-year degree. Possible to get hired without the degree, but the deck is stacked against it.
You could also likely get hired at one of the LCC's, Jetblue, Spirit, etc. The degree might or might not be a factor.
Being a foreigner will not hurt you in any way, in fact I suspect that once a foriegn person gets a green card (and FAA certs), US airlines are actually more likely to hire him to avoid any suspicion of discrimination... we have a lot of foreigners in the US airline business.
You will need to convert your licenses to a US commercial ME, but then the regionals will provide the additional training for the ATP.
It would be possible to work for a regional and obtain a degree via distance learning. The big majors in the US should still be hiring in large numbers by the time you wrap that up.