Nice project. I did something similar a while back when I had my Tobin 16 restocked in English that looks like it came from the same tree. I didn't do the whole nine yards, like you are doing, but, fitted it up to my dimensions with my prefered straight hand stock. Stan Baker saw to it that the gun worked with contemporary ammunition, with chokes of IC and MOD, from FULL and E-FULL, and the barrels were re-blued. The case colors are faded, but, present, and I left some of the original screws that had seen better days in the gun just because they had been there about 100 years. I didn't want to remove all the evidence of the life it had seen, just adapt what was there to my needs and use. I really enjoy mine.
I've been in pheasants, and pheasant hunting conditions as you described, and have wished on several of those occasions for a light ten loaded with 1 1/4 oz of 2s, but, the 12 is the most logical choice. Ignore the questions about why you can't do that hunting with a 20 or a 28, a few here are talkers, and not doers. Make sure it fits you when you are wearing a coat, it isn't your early season woodcock gun, after all.
And keep us posted. Looks to be a fabulous start.
Best,
Ted