Marlin, yes that is a great gun and not many around in the condition shown here.
The serial numbers for hammerless Syracuse guns started at 16000 in August of 1886, so I would estimate your gun as being from early 1887.
The Trap butt plate was an advertisement showing that these guns were good in the field as well as at the Traps.

Please if you would could you give me the barrel length for my records and anything else that might be of interest, thanks.