I wonder if it is possible to check luggage at a later point in the trip? If you are boarding at a smaller station with no checked baggage, but another station en-route does have checked baggage, if you could arrange to hand off your bag at that station to the baggage attendant and check it the rest of the way?
Unless it was somewhere like San Antonio or Spokane with a multi-hour stop, you wouldn't be able to meet the 45 minutes before departure deadline, but maybe this would be a service Amtrak could offer; you board and put your bag on the storage rack, then arrange with the attendant to tag the bag through to your destination. At the next checked baggage stop, either they move it for you or you grab your bag and take it up to the baggage car and hand it to the attendant who is loading the car, tears off your half of the tag, and loads it. Then you get back on the train. (Any station that handles checked baggage has to have a stop that is long enough to load and unload it, so you should have time.) Or maybe hand it off to a Red Cap if the station has Red Cap service.
Unless it was somewhere like San Antonio or Spokane with a multi-hour stop, you wouldn't be able to meet the 45 minutes before departure deadline, but maybe this would be a service Amtrak could offer; you board and put your bag on the storage rack, then arrange with the attendant to tag the bag through to your destination. At the next checked baggage stop, either they move it for you or you grab your bag and take it up to the baggage car and hand it to the attendant who is loading the car, tears off your half of the tag, and loads it. Then you get back on the train. (Any station that handles checked baggage has to have a stop that is long enough to load and unload it, so you should have time.) Or maybe hand it off to a Red Cap if the station has Red Cap service.