Can't suggest anything that has not already been suggested.

But I can say that if I am planning to sleep indoors after a train ride or flight, I make my reservations the same day I get my ticket to ride or fly. I usually have both options settled and then make both reservations.

Camping, I almost never make reservations, but more often than not do when sleeping indoors, which includes hostels in large cities.

When I took the train to Whitefish Montana in 2012 and the train was going to arrive after midnight, I called the motel I had a reservation to let them know I would arrive after midnight. They said, it is a good thing you called, we close the office at 11pm, so we will leave an envelope with your name on it with the key and they told me where to look. Got there after 2am and the key was in the envelope where they said it would be. My point is when sleeping indoors, it pays to get your ducks in a row early and keep them there.

This says platform, no shelter, waiting room closed after 11:59pm. So no chance to sleep in a train station. But this says no baggage service, so is your bike in the train car with you as luggage?
https://www.amtrak.com/stations/rsp

You were not clear if you are not camping at all on this trip, or it was just the first night you do not want to camp. There is a roof overhang in the photo, perhaps use your sleeping bag there if you bring camping gear?
https://www.amtrak.com/stations/rsp