Amtrak already has a variety of load management pricing schemes in place. A trip between Boston and NYC has base prices ranging between $54 and $95 (before adding in special discounts, group discounts, first class supplement, etc.)depending on time and day of week. This practice is hated (for no obvious reason beyond their general hatred of rail travel) by the Republicans and every year of the Bush administration the Amtrak funding bill has included a section to eliminate this practice. Every year it gets amended out and the load management continues.

As for "abysmally low" you should check the ridership statistics and not the press releases. Ridership varies widely by route, and for several years has been increasing steadily on the popular routes. The Acela routinely runs sold out at peak travel hours despite the price differences. (I use it. It's a business expense, still cheaper than flying, so I don't care that I pay top price. It's the tourists that time shift.)

Amtrak does have a small group discount policy for groups of 4-6. The availability is limited and percentage discount varies. They do try to sell those empty seats. It is not available on Acela, which is no surprise given the frequency that Acela sells out.