I don't think there's much chance you'd be able to get your bike on that train.

Regarding the 28x22x16 size restriction: I've seen plenty of large, oversized bags as carry on bags on Amtrak. But they're bags. Bikes is another matter, and they'd most likely balk at someone bringing a full size bike as carry-on baggage. Amtrak allows true folding bikes as carry-on on any of their trains. From what I've heard, bringing a full-sized bike as a carry-on is "conductor's discretion". I doubt that a conductor would allow that on one of the busy, crowded routes in the Northeast Corridor. And if you did manage to get it on with the conductor's approval, the problem that could be encountered is on longer routes there are several different conductors. So you might find a sympathetic conductor when you get on, but then there could be a crew change and the new conductor could boot your bike off.

If you wanted to try bringing your bike with you on the train, you could take the Lake Shore Limited train from NYC to Buffalo, get off and ride across the border at Niagra Falls, then hop on a VIA Rail train to Montreal from there. It would definitely be a lot longer, but it's the only feasible option I know of where you could bring the bike as checked baggage.

It's a pity, though. The Vermonter (the route that goes through Vermont to St. Albans) used to allow bikes and skis in their baggage car. Then Vermont cut the funding for it.