Hey, Rich: I could recommend two sections, both of which are in Maine. My first choice would be the West Branch Penobscot River, with one night in Lobster Lake and then 2 or 3 nights down the river to Chesuncook Lake. Camping is first-come, first served but usually it is pretty easy finding a site. You can make arrangements for a vehicle shuttle with Chesuncook Lake House. Or, try Mooselookmeguntic Lake and Richardson Lake (there is a real short portage betwen the two). You’ll have to reserve campsites ahead of time on both of these lakes though.
The Connecticut river may be a possibility. Only part of the trip would be on the NFCT but I think there is only one short portage at wyoming day.
I don’t know how many canoes you’ll have but you could also do a trip in the Adirondacks starting up in the Floodwood area of Upper St Saranac Lake and ending in Saranac village mostly on the NFCT. I think you can rent a couple of carts Raquette River Outfitters that will make the .6 mile Bartlett Carry very easy, they’re great folks and offers shuttles and free trip planning as well.