I'd jump ship to get on with a regional/national as soon as possible. My class was made up of 1/2 civilian. Two of the civies had G-IV international experience with large fortune 500 companies. The other civies were all regional jet guys from Mesa, Pinnacle, ExpressJet, COMAIR, Eagle and Mesaba. There was one guy who didn't have any jet time at all. He was a Dash 8 Captain, PC Check Airman, Simulator Instructor and had been an intern at FedEx during college. If my class is the norm - the norm says go get your jet pic in 121 for a higher percentage chance at FedEx. Of course, if you have flight time in aircraft over 150K/lbs, glass and FMS time you'll be quickly picked up for the MD-11 ANC if they do what they did last time. The majority of the civies in my class had 4500-6500 TT, former Line Check Airman, Simulator Instructors, Chief Pilots etc. Two of the civies had 9000+TT with over 4000 JET PIC in a 121 environment.
Maybe that intel will help you make the choice you need to make.
Best of luck!