I've never taken shelter on this trip, I camped under the stars on night 1 and in the Lunksoos leanto on Night 2.  Wonderful weather blessed us on both previous trips.  Sleep "under the stars" under a rainstorm would suck.  There are a total of 3 leantos within Kathadin Woods and Water - they can all be seen on their map, on their webpage.  The first night was in Baxter (no easy to get to leantos), which is the only night you will need to pay for a campsite and also need to make reservations.  Or you could ride straight through the park on Day 1 and camp just inside the north border of KWW.  Baxter is beautiful though, so it may not be the coolest thing to do unless saving some coin and skipping the red tape is preferred. 

I've never ridden that area of the state, it's a further drive for me than going to areas near Millinocket or Lincoln for instance.  But I've driven through that western part of the state and it's a beautiful region for sure!  The best looking routes in the Gazetteer are likely those that traverse private logging land, you should check and make sure you are not violating the no-bikes (motor included) in those areas before heading out.

There is another thread in the forum called "Maine" that you should check out - might give you some alternative ideas.

- Baxter does not allow riding on any of the singletrack in the park, ONLY on the Tote/Loop rd.  Some of the singletrack in the park is beautiful, too bad it's off limits.
- Higher elevations on the IAT are, like you say of the Maine AT, not practically built.  They are often a-b as fast as possible, no switchbacks.  So there is lots of hike-a-bike but the descents are pretty rad.  The lower elevations often utilize old logging roads and so the riding is pretty decent, though overgrowth can be an issue.
- The IAT within Katadhin Woods/Water allows cycling on all the old roads including those used by the IAT.  On the singletrack portions of the IAT it's not "sanctioned" nor is it "unsanctioned", so we need to tread lightly for now.  I've been talking to the park's rec managers and am trying to delicately figure it out.  I don't want to open a can of worms!  Talking to the Maine Chapter of the IAT would be the next logical step, to secure the rest of the trail through the state. 
- I have no idea what the terrain is like in Canada's portion of the IAT or what those trail orgs think of cycling on the trail.  It would be an amazing journey, going from Katahdin all the way through the NE provinces of Canada.  Would love to do it.  I think it's safe that no one has ever done it before either!!

It may go without saying, the best time of year to do this is as soon as the winter ground dries or in  late-summer into autumn.  Otherwise you're likely to enjoy a deep wood buggy overgrown experience!

No supply along the route unless you go off track by a bit to the Matagamon Wilderness campgnd/store/deli (near north end of loop, http://www.matagamon.com/).
I've always taken all my food, easy campfire food or no-cook stuff, and purified H2O along the way.  Or fish if you are any good at it, Penobscot River offers famous fishing ops!
Ultra light packing will make the hike-a-bike sections MUCH more enjoyable - I did it on my fully loaded cross bike the first time, it was awful. The last time I was on my fatbike with hardly any supplies and the experience was wonderful!

I think you can see these routes, let me know if not and I will chg permissions:
It's mostly this route: http://ridewithgps.com/routes/5800262
With just a bit more IAT singletrack that I rode in this one: http://ridewithgps.com/routes/6271918
Start / Finish in Millinocket.
That's it, work is done.
Oh, go to the IAT Maine Chapter webpage, there is an excellent map there that you can download/print.  It covers most of the area where getting lost would be a concern.

There are two awesome options in Maine, the first more civilized and the latter more wild!

1) Mix the very awesome (approaching KT quality) singletrack network in Carrabassett Valley (CV NEMBA) with the lodging/tenting options available through Maine Huts & Trails.  You could build a 2 day to short 3 day trip easily I think.  I've never overnighted here, only done 1 dayers.
- Pros: superb singletrack and well-maintained trails, uberposh accommodations if you choose to lodge with Huts&trails, or simple tenting, minimum tarmac, vistas of Bigelow Range.
- Cons: you're likely to see other folks, you're riding in somewhat of a confined area and never far from safety/civilization
It's entirely possible that the bikepacking in Carrabassett could be lengthened and made more wild, I'd have to look at a map more closely. 

2) Start in Millinocket - Mix the beautiful dirt Tote Rd in Baxter State Park (maintained but rough) with the old/unmaintained logging network of Katahdin Woods/Water (future NP maybe) with the Int'l AT (the most beautiful and ultra-challenging bike-legal singletrack in the northeast, seriously) and finishing on maintained logging roads leading back to Millinocket.  This is a minimum 3 day trip, 4 days would allow a more relaxing trip and time to explore if desired, probably 120mi total, depends on variations.  I forced this into 2.5 very hard days last time I went.
- Pros: wild! (you will feel as though you are riding where no one has ever ridden before!), once on KWW land (1/2 the loop) you are unlikely to see another human and far from civilization, above tree line singletrack, vistas of Katahdin range, follow Thoreau's route along Penobscot's E Branch.  Free lean-tos available along route so no need to lug shelter.
- Cons: some tarmac riding (between Millinocket, your base, and entrance to Baxter - 10miles total), all of KWW is unmaintained (wild comes at a cost) so expect challenging navigation, the only singletrack is on the IAT (it will treat you with beautiful views and ripping descents, you will pay with extreme hike-a-bike).
I'm partial to this tour, but that's because I like being lost and feeling like a real adventurer!  I'm rather certain that my buddy and I are the only ones to have ever ridden the IAT and from what I know less than a dozen folks have ridden the KWW network.

Either way, I'd love to join you if possible, please let me know!