There are minimums and then there is competitive. Competitive at Dynamic is closer to 4000TT with prior military flying experience, or 6000TT with experience flying their types.
I worked along side a govt contractor operating a king air, and I asked what ther pilot group looked like... They had 13 pilots, 11 were prior military pilots with at least 2000 hours when hired. One was a prior special ops guy who got his civilian ratings. The last guy had no military experience but had several type ratings including 747 and over 15000TT when hired. You might just have to bite the bullet and go to a regional to build up some time before those goal posts move to 1500TT.
Remember, lots of the guys going to these jobs are prior military pilots, how have flown in the AOR doing similar type missions, over 2000TT, and include guys who have already done ISR, special warfare, etc... I met one guy trying to get hired at Airscan and he was a pilot in the 160th SOAR, just to give you an idea.