The general rule on Amtrak, for coach travel, is that conductors are happy to get any piece of paper from you once you are on board.

This applies even more so on unreserved trains. For example, if you purchase a ticket on an unreserved train on Amtrak's website, it will ask you to specify a date and a particular train run, but when the tickets print out none of that information appears, and it just says "unreserved".

I would not even have a problem with boarding a reserved coach train with a ticket for say, the next day, if the train is sold out and they refuse to sell tickets. Amtrak does not typically assign seats, and "there is always a seat somewhere".

The only cautionary note would be at stations that collect tickets ahead of boarding a train. As things get more bureaucratic, there is a chance that somebody will actually read the ticket.

I suspect what will happen in your case is that the tickets will not specify a date of use. They may have the usual "not valid before" and "not valid after" dates (usually the first date is the first date of travel, and the last one is 6 months later".