Ken there are many questions that need to be addressed but unfortunately there is no one surviving that can help. It is stated that Hunter Arms Co. started in 1890 when in fact it started in 1889. Syracuse records are lost or someone is holding on to them.
If you had or anyone has read Houchins' book he states that the Syracuse hammer guns ended at serial number 25470 but I have serial number 26397 c. 1889 that has L.C. Smith Maker on the barrels and has the squared lug of the Syracuse guns. I do have other hammer guns with the squared lug but was not able to see the top of the barrels (auction guns) to verify maker. I have serial numbers up to when Hunter Arms Gun Co. started making hammer guns and that started below serial number 26469 that now has the rounded lug but still no makers name on barrels. These serial numbers go all the way to 29992 with no makers name on barrels. Starting in 1890 is when the records for Hunter Arms started at 30,000. In 1891, 1892 and 1893 there were on hammer guns made and I wonder if that was for re-tooling. Also Syracuse was only making hammer guns in 1889 with serial numbers 25,000 and 26,000 with no guns found with 24,000 serial numbers. Serial numbers 28,000 and 29,000 have the rounded lug again with no makers name and I believe some of the squared lug hammer guns were sent to Fulton to be assembled with machinery, tools and unfinished guns.

As to your serial number, you are correct, I do not have it, the serial number would make it a Hunter Arms gun made in Fulton. The bottom of the barrels on some of the higher graded guns has XX or XXX and again no one seems to know what that means although some speculate it could be the barrel grade of steel or Damascus they were made of.

As to pictures, I used to use Photobucket but then they wanted money so I switched to Imgur which was great but now they must have changed something because I cannot edit the pictures I download into it. I can send them full resolution but who wants a picture that takes up the whole screen.