I admit I have trouble thinking in drams. So taking the information from the Mid 19th century chart you provided, I converted drams to grains for each gauge listed. I thought it might be interesting to compare the recommended load of shot to the weight of a bore sized round ball in each gauge and added that.
20 Ga, 2 drams = 55 grains, ¾ oz. shot
.615 Round Ball = .800 oz.
16 Ga, 2 ½ drams = 68.75 grains, 7/8 oz. shot
.663 Round Ball = 1 oz.
14 Ga, 2 7/8 drams = 79.06 grains, 1 1/16 oz. shot
.693 Round Ball = 1.143 oz.
12 Ga, 3 drams = 82.5 grains, 1 1/8 oz. shot
.729 Round Ball = 1.333 oz.
Note: The recommended powder granulations for all these calibers was either FFFg or FFFFg
So it seems in 20 and 16 gauges, the weight of the shot load is a bit less than a bore size round ball. However, in 14 and 12 gauges, the weight of the shot load is more than a bore size round ball.
I do wonder what kind of pressures these charges developed?
Gus