It should not cost you anymore to ship it to Japan because even if he lives off post/base they will have an on base/post box, thus it would be the exact same cost. The only mail when we lived off base that we ever received were the utility bills for the house we rented. The rest of all of our mail from the states went to APO Box 6944 AE XYZ12....funny I can remember the box number 20 yrs later, but not the zip.
The way the cost is determined if I recall correctly is you will be charged the cost to ship to that FPO zip code. For example, when we lived in England ours was an AE and the shipping was out of NY, so the cost was not ship to the UK, but just to NY. I believe the Pacific (AP) all went out of San Francisco.
USMC is correct they have a date for Xmas to guarantee arrival. The reason why is because they will send it to one collection base. Ours was Germany, and from there it is routed to the actual base, which added a few more days into the travel time.