There is plenty of parking along Railroad Street in Gorham. The Town Hall is on Park Street in Gorham which is one way. Every local cop and quite a few state cops drive up one way Exchange Street onto Railroad street past cars parked on Railroad Street several times a day when they head to Town Hall. Park near the town Library or across the street near Town Hall. I would suggest going into the town hall and letting the police dispatcher know you are parking for long term and your plate number. The town just bought a new building on Exchange street with a big parking lot but I would check with the dispatcher to see if they recommend a specific spot.
Note the AT does not go into Gorham it skirts around town and crosses RT 2 in Shelburne. I would not leave a car long term at the AT crossing. It a 3 1/2 miles from the Town Hall to the AT crossing. There is a way to walk directly into town via the former AT route via the Mahoosuc trail but most section hikers take the current route (the Centennial trail). Its usually an easy hitch to the US2 crossing.
$500 for the shuttle
http://www.trailangelshikerservices.com/. They advertise the BSP office which actually is 45 minutes from Katahdin Stream Campground in Baxter. Ideally you would end up staying at the AT Lodge and getting a ride in the next day. Its about a 4.5 to 5.5 hour drive from Gorham to KSC.
The bummer is folks are driving back and forth this way frequently but lining up with when you want to go is the problems.