What a great idea!
First, you have plenty of time to plan and to do the ride. If you want to do a route that is completely laid out, fine, But if you want to combine pieces to make your own route, that will work, too.
Second, you should consider where YOU want to start and end - rather than let a route dictate. Generally speaking, it makes little difference in surface winds eastbound or westbound. That said, there are a few places westbound that you might encounter stiff headwinds - the High Plains, the Columbia Gorge. I'd say it's 55/45.
Third, a 3600-mile trip will take 10 weeks if you do 5 days at 72-miles, 5 1/2 days at 66-miles, 6 days at 60 miles. A very doable pace with time built in to explore, take a break, or deal with the unexpected.
Fourth, consider the weather where you might be each month. A late May start eastbound should probably be from central Calif. Westbound would be best from the Chesapeake/Delaware. That said, late June thru early August can be brutal in the Great Plains and the Mississippi & Ohio Valleys. Plus in the West you have climate zones running north-south that vary greatly from desert to alpine.
I have done a half dozen x-USA traps - some years the central U.S. has been reasonable, other years it has been scorching. A trip that stays in the northern Plains and hugs the Great Lakes is likely to have more pleasant temperatures. If running into other cyclists is something important for y'all, then yes, the TransAm would be best.
There are lots of designated routes besides the ones listed at ACA - other cross-country routes and state-supported bike routes, too. The nice thing about putting together your own route is that it really becomes your own. If you wanted to start at the Capitol in Washington DC and end at the Golden Gate Bridge - - then why not?
Feel free to ask me any questions - -