I think a problem you'll run into is the amount of time it'll take to travel with trains. Doing a rough calculation, including some of the "possible" destinations, around 8 days would be spent on trains. Of course, another problem with planning such a broad trip is that you'll be rushing around so much that you won't have enough time to spend in each place. Cities like New York, Chicago, Washington DC and LA demand at least 3-4 days to experience properly, and that's not even mentioning other great cities like San Diego, Philadelphia, Atlanta and Denver.Would someone who has actually visited these facilities or planned a trip like this do it similarly or have I got it all wrong in terms of time, scale and price?
For what I believe is your first major trip to the US, I'd recommend a shorter, more focused trip (for example, New York, Philadelphia and Washington DC over 8-10 days). A trip like this has the benefit of being cheaper, much easier, allows you to see each place properly and doesn't mean you spend 8 days on trains