Also, it depends on your budget. We met a couple of guys from the Netherlands who only rode with a rain jacket as additional gear. They rode hotel-to-hotel 60 - 120+ miles a day and ate in restaurants. They were fast!
On our W-E trip last summer, we found that many small towns had lost their grocery store because there's a Wal-Mart 25 or so miles down the road, easily accessed by car. Some significant number of small towns have had their grocery "replaced" with a Dollar General. We found them to be a good source for peanut butter and trail mix. I ate more trail mix last summer than in all of my prior life combined, LOL.
We also carried lightweight cooking gear and bought a few days worth of relatively nutritional items that we could make into a one pot meal. This included cooked chicken breast in pouches and pre-cooked Uncle Ben's rice in a variety of flavors (also found in pouches). We also carried flour tortillas and peanut butter. A great lunch is a flour (whole wheat) tortilla, peanut butter and roadside wild blackberries.
You can make a very lightweight alcohol stove and carry pretty minimal gear to cook with. Consult the ACA TransAm maps to see where there might be "holes" along your planned daily rides and plan accordingly.