I can understand how this could make a person nervous. I've known people that spent a small fortune for a headstock..
"the neck cleanly broken off along the grain through the foot just below the top of the instrument. The owner has received a $3500 quote for a neck graft".... so you don't want to check it.
Considering most professional grade string instruments are no less than $25,000, nervousness is warranted.
Last time I traveled with a cellist on the NEC, they had an additional seat purchased, though our group numbered 6 plus instruments.
I’ve asked a few colleagues, and all of them have said to purchase an additional seat, though one who’s a little laxer did say they were able to lay their cello flat under the first rack of luggage at one point.
In my experience, what Amtrak or and airline has listed on their site isn’t necessarily what one will experience in person. I’ve had general luck over the years, though I’ve had plenty of colleagues who’ve not.
I don’t know what your cello is. If you have a fine instrument, and booking an extra seat is not an option, I suggest making sure you keep a copy that page of the Amtrak site on you, and asking an attendant for help.
Whether you travel or not with your instrument is up to you - and how much risk you can stomach.
That said, trains are ALWAYS less risky than flying.