Rather than spending a couple of months training for the FI(r) and about £7000 and then four months teaching students, why dont you pool your money and put in some multi time in the US and keep busy that way.
You might not even get to do that much teaching of students because by the time you finished the FI course, the autumn would be on us and you might only literally get a couple of hours in before you are off to your airline jobs.
It seems an awful lot of money to spend for so little in return.