When Rambler and I did it in 2004, we did another variation:
We spotted the car at Abol Bridge (the store people told us where to park). Then 8 days later when we got there we camped the night at the commercial campground (ask in the store) although some folks we met on the way camped across the road at the State campground.
We replenished some stuff from the car, and ditched some stuff (like the tents) then hiked to the Birches the next morning.
We summited Katahdin the next day, but decided on the spur of the moment to come down via the Knife Edge and Helon Taylor trail and hitched a ride from Roaring Brook - we just went to the parking lot and asked whoever was getting into their cars. Second car we asked was good. We convinced the car to drop us at Abol Ponds (a couple of miles past the gate for them), hiked the mile of so out and we were back at the car.
BTW: those who decide, as we did, to descend via the Knife Edge - we found it was very easy to hitch back. Go for it!
And for those who return via the Hunt trail - it's also an easy hitch down to Abol Ponds and a short hike back to Abol Bridge.
Another aside - We stayed a night at White House landing (and picked up a mail drop). Highly reccomended!