Ron, what a treasure!
questions that need answers:
How deep is the rifling?
What is the bore and groove measurement?
That will help you on bullet diameter. A grooved and lubricated bullet will obturate considerably, but the close it can be to the groove diameter
to start with, generally the more accurate it will be.
A 26" ROT in a .56, will support quite a long bullet, actually, in the 600gr. range, maybe more.
We know that a .50 cal. with 24" ROT will shoot very accurately to 1000 meters with a 600gr. bullet.
In .56 cal. it should shoot any 'conical' well, I would suggest from 400gr. up. The longer the bullet,
to some extent, the better the long range accuracy should be.
At the turn of the 19th to 20th century, Harry Pope, both a 'rest" and standing shooter, noted that a Man's offhand rifle should be 16 pounds, and a woman should be shooting
a 12 pound rifle. IIRC He was talking "Schutzen-style rifles".
This bullet gun is not one of those and like you said, likely a bench rifle. If meant for offhand shooting, it would have had a hooked plate to assist with holding the rear of the gun to the shoulder.
The rod's short length is interesting and confusing.