Welcome to the ACA Forums.
Try posting in the "Companions Wanted" thread in the Classified section.
While you think crossing the country by yourself is daunting, several hundred people have done it each year for the past 50 years, literally. I would guess that at least 33% of people doing it are riding alone. Maybe 50%. Anyway, here is a suggestion for the most traffic-free published route:
Start in Washington, DC, and ride the C&O Canal Path to Cumberland, MD (can be a bit bumpy as it is almost entirely unpaved but is definitely doable.
Connect to ACA's Chicago to NYC Route to Indianapolis
Connect to either ACA's Eastern Express Connector Route (excellent maps and more riders) or a quieter, less traffic, and more scenic alternate route I created
https://ridewithgps.com/collections/2244653 . Both end at or near St Louis.
From St. Louis, connect to ACA's Eastern Express Route to Atchison, KS.
From there you have two options:
Head north on a flatter, less traffic route via ACA's Lewis & Clark Route to Chamberlain, SD then west on ACA's Parks, Peaks, and Prairies Route to Yellowstone where you connect with ACA's TransAm Route.
Head west on the Eastern Express to Walden on a hillier route where you connect to ACA's TransAm Route.
Sure, the above routes will be places with higher traffic but overall, it is fairly low traffic and has MUCH more paved roads than The Great American Trail, which is actually not a completed trail but more of a concept.
Take a look at this ACA Interactive map
https://www.adventurecycling.org/routes-and-maps/interactive-network-map/. It shows all of ACA's routes. If you want routes in a different area, just ask and one of us probably have a decent suggestion.
Tailwinds, John