Great question. In my opinion, mailing food or equipment is a waste of time and money, and a detriment to the local economy. Everything you could ever need on the NFCT to cook nutritious, delicious food is available at the grocery store in the towns you paddle through. Buy from them. Carry a half dozen ice bags or other durable, tall, non-ziplock bags and rebag in the parking lot. Toss the superfluous packaging.
Better yet, this can mean you never need to carry more than 3-4 days worth of food at a time. At 1.5 pounds of food per person per day for a single tandem boat, that is only 9-12 pounds of food per leg. Plan portages through towns and hit the supermarket. Print out store hours (and other pertinent hours, like library, sandwich shop, etc) and carry them with your documents. From Jackman to Allagash Village is the longest stretch without a good grocery store. Rockwood has a general store with most of what you would need, however.
I did the NFCT in 2007 in 32 days, and carried between 3-4 days of food at a time, with 5-6 days of food for Moosehead to Fort Kent.
For two 19 year old men (boys?) we ate very well with 70 pounds of food, costing $450, and taking about 5 hours (over a month) to plan, purchase, and pack for the entire expedition.