Shaw made a 1/36" barrel for the Black Eagle, with sights. All the SBE were 1/28" and no sights. I have had Shaw make barrels for me and have talked to them often. I also have had the Black Eagle 1/36" and it was not impressive.
I have two and have drifted to muzzleloaders. I sent a shot barrel/receiver to Shaw and had them install a rifled barrel on receiver. Any interest? Open to offers.
There is a range of bore diamaters that meets the standard of a 12 gauge, SBE leans towards the tighter side. They feel their market is for what they make. Berretta runs middle of the road and Browning seems to go large. I do not know how many different makers have same diamater, less than you would think.
E R Shaw is still in business, do a internet search. That barrel should be a SBE(will fit a SBE II) barrel. They made slug barrels for Benelli for many years. It has heavier walls than newer barrels and needs a special forearm, or sanding for stock forearm. It is a 2 3/4 or 3" only barrel. A valuable and good barrel. Do you want to sell? I know people looking for them as around here there are few rifle areas.
A SBE barrel will fit a SBE II. Newer barrels have a longer mounting tab on the magazine ring but you have a forearm to match slug barrel so there can not be any problems.
The only part I question is"And wads separate from the shot within a foot or two of the muzzle, and are then a non-factor". If they push the shot after the muzzle at all they must have some affect.
The ring and upper reciever are repairable. To get a custom left hand slug barrel made I had to supply a factory shot barrel to obtain these parts. They are not a seperate items you can order. Most manf. will not return parts if any warranty is given. A disconted barrel is considered giving warranty service. If parts were returned the ring could be repaired by many gunsmiths and then used w/ buldge.
I have found magazines that have ammo left loaded tend to weaken the spring and cause mis-feeds. If it has been loaded that long the magazine might be junk.
I will answer your questions w/statement of what I know.
Newer barrels have a longer mating surface of the magazine ring. This can cause forearm fit problems w/older gun and newer barrel combo, forearm can be modded. The newer barrels have rifle sights. I think the newer barrel will fit stock forearm. The older barrels(marked and made by E R Shaw) do not have rifle sights. They have a thicker wall than newer barrels and require a SBE I slug barrel forearm. The shot barrel(SBE I or SBEII) forearm can be enlarged to fit a old slug barrel.
It comes tapped on the reciever, no cantilever mount. It takes a standard scope base. That is the nice part, a good scope mount that goes with the barrel assembly. The fast twist rate makes it a first class slug gun. The bad part is they put rifle sights on the barrel and they can get in the way. The old barrels made by E R Shaw did not have rifle sights but they are only avail. used and there are very few for sale.