Mark,
I don't know about Fox guns, I do know about L.C. Smiths. From the begining production of the 16 ga it was chambered 2 9/16" and the bores were .650. From a record sheet of June 3, 1936 chambers were still 2 9/16" but bores were then .662. Some say the chambers were changed close to then also but I have a 1939 still with 2 9/16" chambers.
The only real way to tell is to use a gage like Skeet's that lets you go into the bores 12". I don't know what their 16 ga. ring is set at, but after zeroing the dial to that ring, inserting it in barrel and withdrawing slowly reading dial will give you the amount of contriction.