In The World's Fighting Shotguns, author Thomas F. Swearengen (CWO, USMC, Ret.) details the evolution of fighting shotguns, including the Remington 870.
There is no mention of manufacture of the 870 in 16" barrel length. There is, however, some information which may be pertinent. In the section on the Ithaca Model 37 he relates that the L.A.P.D and L.A. County Sheriff's interest in shorter barrels led to an (initial) recommendation of an 18 inch barrel length and that:
"...some Remington 870 and Winchester Model 12 guns had their barrels cut to this length during the tests. These modified guns displayed an average overall length of about 38 inches (96.5cm). It was decided that this length was still too great for safety, but was within maximum acceptable tolerances. A total length of around 36 inches (91.4cm) was the desired goal."*
"During 1965, the Los Angeles County Sheriff's Office negotiated with Ithaca to produce a special short-barrel variation of the Model 37DS Police Special...equipped with a 16.25-inch (41.3cm) barrel."**
"The overall utility of the modified Police Special caused other west coast police departments to begin favoring the same gun, which further brought it to the attention of other departments around the country. This activity offered some keen sales competition to the Remington 870P. It was during this period that the Model 37 DS Police Special and the Remington 870P became the two most common police shotguns in the United States."***
*Swearengen, page 263, The World's Fighting Shotguns
**Swearengen, page 264, The World's Fighting Shotguns
***Swearengen, pages 264-265, The World's Fighting Shotguns