I have an underlifter, made in 1874, and its bores are .75 (11 gauge) bhut the chambers are for 10 gauge shells. Spoke with Mr. Hoover, who wrote 2 very interesting articles about Parker 11 bore guns. He said some had 12 ga, some 11 ga, and some 10 ga chambers. I also have a DHE, made in 1889 that has 12 ga chambers, but overbored bores, to the tune of about .753 if my memory is correct. But it still measures mod & full with a bore gauge, so it may also have been an 11 bore gun. Seems best to expect the unexpected on some of these guns.

Can we sneak a 12 gauge shell into a chamber made for an 11?

A 12 ga shell would be very loose in an 11 ga chamber, but some of the 11 bore guns had 12 ga chambers.