Don't wait til you get here to visit the FAA. Download the foreign pilot verification form posted in North America, and send it to the FSDO near where you want to train. As for the DOJ background checks, everybody says it's impossible but mine took one week exactly. The company faxed a form to the DOJ and got it back a week later and I started Indoc the next day. (i'm an ozzie). So I don't know what all the fuss is about.
If you are smart though you will combine a type rating with an ATP ride instead of doing two separate training courses and two separate checkrides.
And Chimbu
"post-9/11 paranoia"
you may not agree with the response but it certainly is not paranoia. 9-11 did actually happen and yes, they are out to get us.