Amtrak's system is terrible when something you want is not available, it usually reports "Sold Out" or "No Train Service" when the actual issue is that there is no train that day, or no facility for checked luggage, as you describe.
They're even allowed to book "impossible" tickets if you're nice (for example, checking a bike to the last station before the one you want that has checked bikes, and working with the conductor to move the bike into the normal train can be done if the train won't be that busy).
That's useful information, and re: bikes something a conductor alluded to on my ride to CHI, when I asked why I couldn't just get off at NPV with my bike which was my actual destination. He was perfectly willing to let me have my bike stowed somewhere out of the way if I hadn't already checked it for unloading @CHI.
What was far more challenging was getting a "trainside checked bike" ticket. The Amtrak web site just kept saying sold out for the +bike option no matter what I tried. But I had no trouble getting the same rate +bike when I went to the SAC station IRL and spoke to a ticketing agent. Apparently my problem was ending the trip at NPV instead of CHI, because NPV can't handle checked bikes. The web site is awful WRT +bike tickets. Maybe this will prove helpful for anyone reading wanting to go ride some distant trails via Amtrak.