I have done several organized double centuries, some 50K road races, and some underground cyclocross events all without carrying any more food than a few power bars in case of an emergency. I don't ever use food stops if available at event rides or any of there services. The lines slow me down and I never like the food selection. I ride self supported from town to town. The only thing I would consider sending to USPS offices is some spare parts, and batteries if budget allowed.
I can do the STP Bicycle classic each year in between 9-17 hours unsupported with very little training. I usually wait for my riding buddies on first 100 and use that as a warm up to go barn storming the second which I have done in under 4 hours. I don't carry anything more than 1 spare tube, Park multi-tool, zipties, and an emergency patch kit. I use about 3-5 20oz bottles of water and gatorade per 100 miles, I eat at subway at 100 miles and snack on fruit and power bars between. I don't even have a bag or rack on my trike, just 3 water bottle racks, and a small Pedros recycle inner tube seat bag for my tube,tool, and patches.
It is very easy to do self supported rides town to town with a few simple reserves like powerbars and hammer gels. I find that eating a good carb heavy dinner the night before helps me as I don't like to start a ride on a full stomach.
You will want to take a good look at the maps. There are stretches of 100+ miles with NO services - nothing.