I would like to do the southen tier, perhaps next year if my health holds out.
As a student I crossed the US both ways by Greyhound on one of those $99* tickets that let you ride any route once in each direction for six months. I deliberately took no reading matter, so that I spent my time on the 'hound listening to people. But I've often wondered if the Greyhound will take your bike, as busses here in Ireland do (mind, it's in the discretion of the driver, so don't try it in the rush hour or after lunch on Friday when the students are going home to the countryside).
But what I hanker for, though I never did it on a bicycle, only a few times by car over fifty years ago, is Autumn (in American English Fall) in New England. The colours of those trees are truly glorious. Won't happen of course, but we can dream of some kind lady who'll undertake to look after our cats and foxes and hedgehogs for a couple of months... On a bicycle you'll have to choose your place and time carefully, probably moving from the Canadian border downwards as the trees turn from the last week in September to the middle of October.
The thing is that practically, my Round Ireland on the Little Roads Beside the Sea, from guesthouse to guesthouse by daily rides manageable on the right bicycle, is much more accessible (for instance, within my cycling experience), planable and therefore possible. I don't see it as a shrinking horizon -- I've been to all the continents and places of note -- but a more detailed progress than the mad dashes of one's youth.
I hope your health does improve, Pavel.
* I know, everyone else remembers those tickets as being a $199, but I distinctly remember that at the time it was $99.