Best wishes for all to go well for you
Though it's been many years ago, I have traveled on Amtrak cross-country a few times, though only coach and not in a berth. But I have some thoughts about your travel.
I hope you will be traveling with someone to help you?
The trains were never as clean then as one would have hoped. Pack disinfecting wipes for bathroom surfaces and such.
As I thought about you walking around on a jerky-train shortly post-surgery, because most surgeons/cardios want post-valve surgery patients to walk a lot and even when traveling, I was thinking about you putting out your hands to balance yourself and thinking about how painful -- and possibly dangerous -- this could be for your sternum, because of the post-op weight restrictions and just the unusual type of strong pain jolts a sawn and wired sternum can send out :eek2:
I looked at berths. As I recall from travel, years ago, these often needed reserved in advance. But you may have already looked into that. You would probably want a private bathroom? Both of the following have such:
This one is designed for a person with mobility impairment
http://www.amtrak.com/media/train_tour/viewliner/viewliner.html with upper and lower berths and a sofa, but you may not be comfortable lying flat immediately post-op.
Smaller bedrooms
http://www.amtrak.com/media/train_tour/viewliner/viewliner.html have seats that convert to a bed, which might work for you -- but due to post-surgery weight restrictions (mine was to not lift or push or pull more than five pounds for eight weeks) you would likely need help with converting them.
Edited to add: I see the links aren't quite accurate (and are duplicates); and you have to click a bit on the links. You can click on the floorplan link to the right. The first berth I described is the accessible bedroom and the second berth is the plain bedroom, both are to the far left of the car diagram.