Where can I get accurate dimensions for the cannon and carriage?I think the best plans are from
Antique Ordnance Publishers. But they are full scale so you would have to scale them down to 1.719/3 = 57.3%. Now that is going to be a pretty big piece, over 3' long. And you will probably need a couple of 3' long drills and a long reamer shank if you plan to ream the bore.
You can cheat on the pilot drill length as you can drill halfway with the pilot, then drill almost halfway with the main drill, then finish the pilot hole using an extension drill holder in the now large hole. If you are in a place with machine shops, see if you can find someone to gundrill the bore for you. That would be much easier. Maybe they would let you watch the process since you are a machine tool student.
What's the best way to mount the cannon to the lathe?You can hold it in a chuck and steady rest for drilling and between centers for profiling; that will be the least of your problems.