Franchi, per the Alliant guide I have, 16.6 grains of Unique pushing a 7/8 oz load with an AA hull, assuming Win 209 primer and the Claybuster 20ga wad (substitute for the WAA20) ought to be pretty close to the 20ga ceiling of 12,000 psi. The book says that recipe, but with 16 grains rather than 16.6, will give you a pressure of 11,200 psi. If you drop down to 15 grains of Unique and use a Remington RXP 20 wad, the book says that will drop your pressure to 8700 psi. If you want to use AA reloads in your Davis, that would be a pretty good formula. You can check the Alliant website to see if they have any other good recipes:
www.alliantpowder.com. You can only go a few hundred psi lower than that with Federal hulls, so if you like the AA's and have them on hand, that's the way I'd go.
The issue with pressure is that most guns built before roughly 1920 had short chambers (2 1/2" in the case of the 20ga) and were not made to withstand the pressures generated by current American factory loads. That did not change until after Olin developed the Super-X in the 20's, and the gun manufacturers started switching over to 2 3/4" chambers as standard.
I would definitely NOT shoot any more of those 1 1/8 oz loads in that gun. That's a short magnum load, and definitely not what your gun was designed to handle. Way more recoil because of the heavy shot charge. Your wood is old; heavy loads can do nasty things to old wood.