Have your chambers been measured by a gunsmith? I believe that most chambers after 1936 were 2 3/4". The Remington game loads and the Fiocchi 16ga shells measure 2 5/8 and will work fine. I use them in my 1924 Ideal grade and they work fine. I was able to adjust my crimp die to crimp the Remington hulls and eventually trimmed all of my hulls down to that length. I have a short kit but it is not needed for 2 5/8 hulls.
Using normal data with the SG16 wads and 1oz of shot you can't get a good crimp. I roll crimp my 1oz loads while 7/8oz loads crimp fine.