CAVU:
Perhaps the rules have changed but when I worked for a US carrier which was heavily involved in military contracts some 15 years ago, I had no problem.
If you have been PV cleared by MOD (as I and my mates had been) then DOD in Washington had no difficulty in checking us out and within a couple of weeks, I had my DOD ID card proclaiming me to be a Field Officer Grade IV and off I went on military charters.