Hi,
I have same EASA quals (military too but not AF), coming here little over two years ago I did FAA CPL+CFI/I (had FAA MEL IR already)...
There is no license validation in CPL level like there is in PPL level so you have to do some training and take the checkride if you wanted FAA CPL - however if you were looking to go direct ATP there is an exemption in the eligibility reqs if you hold ICAO CPL+IR and meet certain requirements (there is one that accounts military experience too), see CFR 61.153.
I believe there is a validation/conversion in ATP level if you hold an ICAO ATPL.