Courtesy of David Noreen
Beginning with the first NID catalogue in 1926 they state - "Unless otherwise ordered Ithaca .410 Cal. and 20 Gauge guns are chambered for the standard 2 1/2 inch shell, 16 Gauge for 2 9/16 inch, 12 Gauge for 2 3/4 inch and 10 Gauge for the standard 2 7/8 inch shell."
Ithaca catalogues for 1926, 1927, 1927-1928, 1928, 1929, 1930, 1931-1932, 1932, No. 50F, and No. 51S, all list 16-gauge as 2 9/16-inch chambers.
By Ithaca catalogue No. 51F the 16-gauge is finally listed with 2 3/4-inch chambers. I believe the catalogues No. 51 equate to 1934.