John-
The following weblog was created by a friend of mine that wanted to do a similar trip in a 1963 Buick Riviera. He discusses many of the logistics issues that you would be concerned about. Se the "Practicalities" tab in his blog.
http://www.ealees.com/roadtrip/index.html
He did his trip in 2 separate ventures of about 6 weeks each. He could probably cover more miles per day than you will in a Model A.
Security surrounding banking, mail, car titleing and registration, etc. have been significantly tightened up since Jon did his epic journey, due to terrorist activities. This will complicate things for you. But it can be done.