Matt from your picture showing the dimension of where the brass casing has left the casing head mark on the receiver face is.975 and probably is a 10 ga. A 12 ga. would be .875+ and an 8 ga. would be close to 1.000.
I'm sure that the receiver opening for the barrel is rectangular with square corners and would be a late Syracuse L.C. Smith or very early Hunter Arms Co., Fulton, N.Y. of 1889. In my records serial number 25470 has L.C. Smith Maker on top of barrels. Most do not when the company was sold in 1889 To John Hunter Sr.
Finding a barrel could be a tough find but they do show up. Good luck.