Washington - Atlantic Coast - Transamerican Trail

[Errio]

Hello,
For next year I start to organise a crossing westbound by the Transamerican Trail + Western Express.
I'm from France, born in 1964, and this US crossing by bike lives since many years in my brain.
Period: may-june 2019. Planned 9 weeks + 1 week security.
I will probably arrive in Dulles airport.

My idea is to get myself + bike driven (bus?) to Washington city. Take a hotel/b&b and take 1 day time to get everything assembled and acclimate.
Then bike south via the Atlantic coast (section 3). Dip the rear wheel in the Potomac bay (it's the same water then Yorktown, isn't it?)
Catch the Transamerican trail 10 miles above Richmond and go west.

Do you think it's a good plan or are there better alternatifs?
In 2010 there was a similar topic, but I did not found any thoughts about this option.

Many thanks, and I hope that my first message was not too long.

Errio, Alsace France