Byron, kick's not cut and dried. Two shotguns firing same weight loads at the same velocity will kick the same if....
The weight's the same.
The weight's distributed the same.IOW, balance affects kick a bit.
The pad is the same size, thickness, material and so forth.
An oz load out of Frankenstein is a creampuff. Medium sized pad, total weight about 7 lbs. Currently, about 14 3/4" LOP.
The 20 gauge YE 870 here runs about 4 oz less, IIRC, and the kick from a 1 oz load is stiff. About 13" LOP.
Some of that difference is weight. Some is LOP, the weight lies out a bit further with Frankenstein and that cuts muzzle rise. Some is due to the pad on the 20 being MUCH smaller, less surface area.
12s run heavier than 20s, all else equal. In your shoes, I'd consider a 12 for turkey, and if kick's that big a prob, spring for a gas auto. The better of these cut kick maybe 40%.
If a new auto is beyond your means, look for a used 1100, 11-87, Winchester X-1 or 2, or the newer Berettas.
HTH....