This thread seems to have come to a natural ending but I do want to share the routes that I've generated using Brouter.

Using app parameters that I came up with for finding the flattest, but not necessarily completely flat, route to my brother's house, I wanted too see what might be coughed up for a cross-country trip such as what the OP is contemplating.

I made only a very few manual tweaks: staying on the Katy Trail and riding the entire Ohio-to-Erie Trail.

Otherwise, the primary consideration would be that this route should be as flat as possible and the secondary one being to find the shortest route. For the original route I generated, using any part of either the Katy Trail or the OTET at all was purely accidental.

Brouter allows you to choose whether or not you're willing to use ferries and this made for a dramatic difference between the two alternate choices.

Hooray. I couldn't upload the individual GPX files previously but I can upload these while packaged together in a single zip file.

Anyway, I used the end of the Great Divide Mountain Route in New Mexico as the starting point and Bennington, Vermont as the destination.