Consistent survival and population net-growth are your most important traits. Everything else you can get to your goals may have to be icing on the cake.
There was a biologist named I. Lehr Brisbon who developed a breed of wild woods chickens in two steps. First, he released several random and common breeds of bantams into a farmyard along with some junglefowl hybrids and allowed them to breed and live freely for several years. Second, he gathered up the survivors and turned them loose into a Georgia river bottom and left them alone for a few years. Over time, natural selection morphed into small, Old English game bantam-like, black and spangled chickens.
You don’t need a woods chicken, just a barnyard chicken. So you can probably just replicate step one by turning out several breeds of homestead heritage and rustic breeds known to be good free rangers and let them breed at will. The strongest will survive. They may morph into directions you aren’t expecting but so long as you keep their size up and don’t let them become bantams they ought to be useful.
You may find that apart from the pleasure of doing the project, American games are already that practical homestead survival bird. You could cross an American to a big bodied oriental game and maybe get that big size you are looking for. Although there are some Americans that push 6lbs already.
