It seems 121 Carriers will only hire Green Card foreigners. They will not accept a work permit, well, the Co. I work for wouldnt.
Expect to fill in a background check form for the Dept of Justice to run thorough background check on you. Takes 45 days and you will need to show up in person to be fingerprinted. It's hard being a non citizen here if you want to fly for a regional or bigger.
WP