the annual permit at Fort Stewart is, or was, 40 bucks and unless its changed its year round for pigs, except during turkey season which runs like 3/20 to 5/15.
You have to have proof of a hunting safety certificate regardless of age, and then you have to either call in or go physically to Pass & Permit office on base to obtain a day pass to a specific area once you have your annual permit.
Hogs are pretty much all over the base, and its in excess of 225,000 acres I believe...but you are right...it would be a lot easier if you hooked up with someone that has experience there.
All the "getting ready" stuff can be done by mail/phone/computer in advance...and there are some fellows who go during the week as well as weekends so you might try posting on the Georgia forum as well here to enlist assistance.