Since this gun will obviously be used for birds, I would find 2-1/2" light 12 ga loads in 7/8 oz, reduce the shot to 3/4" and roll crimp them in 2". If they are around 6000 psi before, the 3/4 oz will be lower.
I have often thought of 2" guns, but I have several English doubles in 12 ga that weigh slightly less than 6#. I find it so much more convenient to shoot 3/4 and 7/8 oz loads in these with 2-1/2" hulls that the idea no longer appealing. What you are doing is shooting a normal English 16 ga upland gun, which is a little more trim and easier to carry in cover.