BTW - Have you looked at the website - Crazyguyonabike?
It is THE BEST resource for bicycle touring - with lots of journals from people who have done it.
Plus a forum for questions.
https://www.crazyguyonabike.com/One of mine:
https://www.crazyguyonabike.com/doc/?o=tS&doc_id=1168&v=sM<<<>>>
When you say spring or fall, I am not sure.
Some people do off-season rides - but the summer months work best for temperatures as well as length of daylight.
400 miles per week is 66 miles per day. (Don't you just hate miles? - 110 km) With one day off or two half days.
You need to plan in time off - for fun, hiking, bad weather, repairs, problems with the pipes, etc.
That said - it will take no more than 11 weeks to do the TransAm for most people.
And early May start from the east will get you to the Pacific by mid July - which is probably as early as you want to do it.
And early June start from the east will get you to the Pacific by mid August - which is probably the best timing E-W.
An early June start from the west can have some tricky weather in the Rockies - nothing too bad, just chilly and wet.
A late June / early July start from the west is probably the best time for the Rockies, but it will be hot in the Plains.
There are some excellent temperature and precipitation maps at the Oregon State Prism website.
http://www.prism.oregonstate.edu/normals/What is it that you really want to see in America? Towns and cities, landscapes, national parks, kitsch?
Do you want to camp most of the time or will you be doing more lodging? Do you like wild camping rather than developed?
Are you willing to do some dirt roads? 25 mm tires are pretty narrow - plus you are only doing double chain rings, right?
I tour on a low-geared, loaded down mountain bike - so our styles may be quite different. But I can go anywhere.
The TransAm is a well-cycled route - but that has its drawbacks as well as advantages.
People along the route have seen so many cyclists that it is nothing new. But they are also pretty welcoming.
You can see a fresher America off the beaten track - more tolerant further north, less so in the Deep South.
There are places in Ohio where you can see the brick pavement of the Lincoln Highway - the first transcontinental road.
There are places in Wyoming where you can see the wagon ruts of the Oregon Trail - where came long before the Lincoln Highway.
It all depends what you want.
You did say 2017, right? So you have lots of time and flexibility.
Best - J