On that same trip I ran into a guy in Bowling Green, OH who was trying to circumnavigate the county using the route you describe, only he was going counterclockwise. The guy was from a suburb of Philadelphia, where I live. After many questions from him, we finally realized that he and I had were on the same club ride to New York City the year before. We had been on the same ferry across the Hudson River and later had dinner with a group of people at a place under the Brooklyn Bridge. I ran into him again at an event the following year. He told me he made it to somewhere on the left coast before packing it in.
Start in the south in early spring and follow spring north up the Atlantic Coast. Hang a left onto the Northern Tier at Damariscotta, ME, get to the west coast by late summer and then head south. Hang another left and cross the south at a time when it will likey not be as hot and humid.