2holer, you have the Batavia Leaders figured out pretty well. Nice helpful pictures, too.
Starting at the bottom of your pics, that is the early Batavia Leader, which by definition should have Twist barrels. At about the serial no. of your gun, the forends changed a bit and the horn tip was discontinued. This model went from 75000 to about 106,000 serial range and was discontinued around 1912, give or take a year.
The middle gun, the 16 gauge appears very late in the Baker Gun and Forging Co. production. Around 1917-1919. A Folsom catalog, before the Folsom takeover, will show that cocking hooke as the "new" design. These guns had Belgian fluid steel barrels. Baker Gun and Forging Co. used a bit smaller frame on their 16 gauges, relative to the 12 ga. This model used the sideplate to retain the firing pin.
The upper gun, as you say, is a Folsom made Baker gun. This model used the original Baker cocking rod mechanism and was furnished with fluid steel barrels. The Folsom made Baker guns seem to have a narrower bar than the ones by Baker Gun and Forging Co. Serial numbers for the Folsom Batavia Leaders are found in the 1F-17,000F serial no. range. Later guns showed decreased workmanship and none of the Folsom Leaders were finished as well as the Baker Gun and Forging Co. Leaders.
