You may as well put a resume together and send it in. The worst they can do is say no.

Incidentally, you ought not spend $12K on your CFII! For half of that you can go to a bridge program and score some jet training and a guaranteed interview.

Another way to do it is to get a job at a local FBO. Work as a CFI, Lineman, whatever and get to know some pilots. You might be surprised at how many people will help you build up your multi time that way.