Surely the people advocating Amtrak are openly mocking the OP. Amtrak? Cross-country? With average speeds < 50mph? With many routes having service just two or three times a week? With on-time arrivals records that make airlines look heroic? The scenic route NYC-MIA?

The TA has identified the problem: too many segments in N America for the typical RTW product. Buying one-way tickets isn't likely to be the best value for money, but logistically is the least complex. If the TA has abandoned hope of helping, I will suggest supplementing the RTW with a circle trip, focusing on routes with a lot of low fare competition. NYC-MIA (or FLL)-LAX-LAS-NYC comes to mind.

Going to HOU to visit a generous uncle in the awl bidness?