Most of the DGS guys are part of the good ole boys club, Most are retired Line check airmen, chief pilots, and or sim instructors.
I have, however come across a few instructors who were none of the above and a couple who were in your exact situation. So don't give up hope.
I highly recommend you make a personal visit to the guy in charge of hiring DGS instructors this is probably your best chance of getting hired.
Good luck!!