"...Might be better to ship at least some stuff, including food, to various post offices and mail store on your route..."

That is what most thru-hikers on the AT (and probably other trails) do. But keep in mind that the Post Office will only hold general delivery mail for 30 days, then it returns to the sender. So navigation would have to be precise enough to get you from post office A to post office B within that time period...