I think I've stumbled onto one of the 16. I bought it several years ago and requested a letter from the Cody Museum. Serial number is in the range listed above and the letter states "Date on record October 10, 1894."
The rifle is chambered in .40-60 on the light receiver. The light receivers came about in 1885. This rifles serial number dates it to 1888 according to the charts.
The stock, however, is English walnut with the London oil (dull) finish. According to Brophy, the English walnut was available from 1891-1896.
I've tried to figure this in my head (dangerous, I know). If you wanted a new large bore Marlin rifle in the years 1892-1894, there was nothing available. The 1893 had .30 caliber offerings and the 1881 was out of production. The 1895 would come out the following year.
I think this was a special order gun made from remaining parts/inventory. The special features were all available in 1894 (but not available in 1888) which supports the factory records.
The records confirm caliber, barrel length and type, and pistol grip stock.
I've been sitting on this hoping to find some other information but haven't run across anything.
Any thoughts?