I just PCS'd from GA to CO and did a Partial Dity and a Military Procured move (or whatever they are calling it these days). I took my SBR's, pistols, Cans, and ammo in my tiny Wrangler. And the movers took my long guns. The contractors took descriptions and serial numbers prior to loading as well as the packers on moving day. They were packed in their original cases and/or soft cases then packed in a larger box and sealed. The outer box contained no identification relating to firearms; only the number ID stickers for the manifest. The packers had no issues with the details and had done it before.
Upon arriving in CO the movers unpacked all the boxes and had me cross-check all serial numbers as well. The one thing that pissed me off about the move in relation to the firearms was at some point all the boxes with serial numbered items were opened in order for someone else to check the serial numbers. I'm guessing at some point when all of the load was transferred between truck to container to truck then delivery it had to be checked.
So if you choose to have the Military procure your move and it will include firearms keep the following in mind:
1. Take your sentimental stuff/NFA items/expensive stuff with you and do a Partial-Dity. (You'll get paid for the weight anyways)
2. Ship only the firearms by themselves. Take off your expensive optics/lights/ or anything easily removed. Likely they will open the box without you there at least once to check serial numbers.
3. Make sure you have your serial numbers, make,and model list with you in case they should go missing AND to give to the contractor prior to the move.
4. Take pictures of the condition of the firearms, the packing process, the people packing, and anything else (to include the ID's of the 3rd party packers/in-packers at pick-up/delivery). When someone knows you've got their name and picture it makes them less likely to rob you later.