Try the Appalachian Trail Lodge in Millinocket, very hiker friendly and they provide some shuttles, I think. Check the trail guides for shuttle services in Monson, I’m sure they’re there.
Check with Baxter State Park about camping. Thru hikers stay at The Birches, first come first served and you sign up as you enter the park, but I don’t know how they define thru hiker. I don’t think the HMW counts. Otherwise you probably need reservations, and they do patrol looking for stealthers.
There are no telephones in Baxter, and very limited cell service. I heard some phones get reception at or near the summit, but not all. There’s a cellular pay phone at Abol Bridge, pretty expensive IIRC. So if you set up shuttles ahead of time, you have to stick to schedule. Depending on season and day, there should be no problem yogi’ing ride to Millinocket from Baxter.
Garlic