Thank you both, moondog and jiejie!
I'm leaning toward just buying plane tickets, but I'm waiting to hear back from my friends as to just how set they are on taking the train. We can buy a multi-city plane ticket for less money, and it sounds like much less hassle.
Thanks for the other train options, too. Definitely something to keep in mind. If we go with the train, I'll contact our hotel ASAP.