Some schools in the US have a program where Canadians can instruct, but for a limited period of time and only if you've done your training there (i.e. UND was like this, likely still is.)
When I was at UND (13 years ago) my fellow Canadians and I got together to form an organization that researched ways to allow us some of the great opportunities our fellow American students were getting right out of school, with no luck. We were allowed a couple of years to stay and instruct at UND (either at GFK or UND satellite schools) and then they punted you back to Canada. There was one guy that convinced Piedmont to hire him as a line pilot, with the understanding that they'd sponsor him for a green card, but a few months later he was back at UND instructing (the story was that it too much paperwork.) Some of my friends stayed by marrying Americans but the rest of us are all back in Canada.
Have you asked the flight school that's offering you the job if they would be willing to sponsor you for a green card? (I'm sure they'd have to prove that there weren't any American candidates which I would expect to be a little tricky...)