I recently acquired a 4.5" dia x 22.5" piece of solid billet steel that used to be the bearing shaft on a large piece of mining equipment...I was thinking of a golf ball howitzer due to the availability of cheap ammo...I got a price from a local machine shop to mill out the bore to 1.723 inches, 20 inches deep for the golf balls.
That would be a good match for the piece you have. To get around the wall thickness=bore diameter rule, you can simply use a 1.5" powder chamber (howitzers generally were chambered anyway.) This means that the bore would need to be drilled (not milled) with two different drills to produce the stepped diameter. The chamber area wouldn't need to be very long to contain a reasonable charge for the bore diameter. If you went with the chamber, firing zinc shot would be practical. Even 1 lb lead shot would be OK as long as you don't use too much powder.