It's called credit card touring. If you do 60 a day just take some time to map out a route that will do about that distance each day and make a series of reservations. Worst case is something horrible happens and you get a long cab ride one day with your bike in the back of an SUV cab. But if you do some net searching I know you'll find a tour group that meets your needs. There are high end fully supported tours with great food and hotel accommodations. I still do all my touring by camping - pitch my own tent, get my water from rivers and lakes, etc etc but I can understand anyone's aversion to the same.