Bob Brister's "Shotgunning The Art and the Science" (2nd Ed.)
See if you can get hold of reading Bob Brister's "Shotgunning The Art and the Science" (2nd Ed.). While it was written in the 70's (?), it's still relevant. I've reproduced some of it below. He delves into recoil from both a physics perspective as well as "felt" recoil.
Briefly, the effective kick of the gun may have little to do with the physics of recoil. It can be that the comb of the stock is too high or too sharp for the shooter. Weight of the gun is another factor. p.99 expands on this.
On that same page, Brister's 125 lb wife is showed firing an Ithaca Mag 10 loaded with 10 gauge 3 1/2 inch magnum loads. How could she handle something like that? A few reasons. One, the Mag 10 is an autoloader. Second, the gun weighs around 11 lbs.
Brister states that for a given load, approximate recoil energy varies inversely with gun weight. On page 105, there's a table that shows recoil of different shotshell loads. Excepting gauge, if everything else about a shell is the same in terms of shot weight, powder, etc., a 20 gauge shotgun weighing 6 lbs 8 oz firing that shell would have 4 ft-lbs more recoil energy than a 12 gauge shotgun weighing 7 lb 8 oz.
Specific to your 20 gauge, the chart says a shell with 2 3/4 drams of powder and 1 oz of shot weight would generate 21 ft-lbs of recoil. Commercially, the Remington Wingmaster HD 20 gauge shell load with #4 or #6 shot would be near this. (I don't know how much powder Remington puts in the shell; the website lists fps instead.)
Very good book. Tons of information no matter your skill level. In closing, I hope this helps.
