I'm not sure I agree with the common refrain here on the forums that most passengers don't care much for domes. The 'modern' interpretation of the Superliner sightseer Lounge certainly seems to be popular with a varied clientele (and corresponding complaints the Amfleet II lounges don't measure up). It is hardly just (or even primarily) railfans who enjoy watching the countryside.The other option that could work but I doubt the owners would go along with it. Tack private cars on for axle count in exchange for free parking for the month. You might get some takers.
And the reason they don't let passengers into the dome when it's an axle count car is actually good business. With only one car you can't guarantee it'll be on the train every day. And you don't want people anticipating an amenity that you can't run on every train or every departure of a certain number. People don't like equipment substitutions especially if it is an amenity they were planing on. But then again most passengers don't care about domes they just want to go to their destination safely, and on time. The railfans do but they make up such a small part of the market I wouldn't worry about them. Amtrak wouldn't miss railfans disappearing as they make up such a minority of passengers.
Regardless, whenever Amtrak schedules the dome on other trains, and thus is expected by passengers, they have no more backup than they would now. It is not good business to leave it closed off - it is a waste. The 'fine print' should always note anyway that specific amenities (the dome) are not guaranteed and equipment substitutions may be made without notice, that's common. I can recall several Southern Railway excursions where I was surprised to find a diesel hauling the train instead of the advertised steam locomotive. Life, and the trip, went on.
The Heritage baggage cars can better fill the role of axle-count cars, but it shouldn't even be necessary. Rusted track isn't exactly a new phenomenon, and other roads seem to cope without such restrictions. Gee, how did they ever manage in the days of the Rail-Diesel Car (RDC)?