Movinion,
For what its worth I was in your shoes two years ago. Left the Marines with about 1900 to 2000 hours and that included a tour as an Instructor Pilot. Most people will have no idea what 2000 hours in the military equates to and those who do will seek you out ahead of the competition.
The unfortunate thing is this; Insurance companies drive the show now. Additionally, if you want to fly for a flight department that is ARGUS rated you are double hosed. Nobody has found a way to break out what constitutes good flight time and what are just numbers on a page. I won't say hours don't mean anything but we have had some pretty experienced guys (meaning they had a lot of hours) that really struggled in the jet.
I can't advise you either way but I can tell you what I had to do. I left the military and got a job at a commuter airline. Take your pick...they will hire you. You will build up hours faster than anywhere else. I would also search out a reserve unit. If you can give this process a year you will be right in the neighborhood of 3000 hours.
In the meantime dust off your suit and start walking into flight departments. Get a bizjetjobs account and pay the annual fee. Look at the directory for flight departments in your area. Send resumes, emails, showup! Start making the connections. It will probably take a year to get your information circulating around the office. Corporate is a tight knit community. It takes a while to get peoples attention.
Chin up and best of luck!
Larry