Nothing obvious, more like something obscure.
There is no reason your checked baggage has to travel on the same train you do, so if the train you are on doesn't offer checked baggage you just need to check the bags for one that does (in this case, the eastboaund Lake Shore Limited). Now, the only problem with this is that the Lake Shore doesn't arrive New York until after the train to Florida has departed, so you would have to send the luggage on its way the day before you actually leave Buffalo for it to reach Orlando the same day you do (and still not necessairily on the same train you arrive on).
That may well not be practical, but as been pointed out, Amtrak carry-on bags sizes (28" and 50 pounds) are fairly generous, and its not like anyone has either a tape measure or a scale to weight the bag anyway. Somebody might well say something if you tried to bring on a 36" bag (the limit for checked baggage, by the way) which felt like it contained a load of lead bricks, but anything fairly close to 28" should be fine.
Finally, no overnight stay is New York (or anywher else) is required between Buffalo and Orlando. The first train of the day eastbound out of Buffalo gets you to New York in time to catch the Silver Meteor south to Florida the same day. Any later train would, indeed, force an overnight layover. Now, coming all the way from northern Ontario, Disney math may well prefer an overnight somewhere along the way. You might need to spend the night in Buffalo to be ready to catch the before 5 a.m. train the next morning, or may opt for a later train (or the Maple Leaf out of Toronto) and overnight in New York to make a more pleasant trip.
It theoritically is possible to make this trip without going via New York, but it would mean driving all the way to Cleveland, Ohio and departing from there, changing trains in Washington.
