I am not claiming any expertise, but based on that little there is available (sources below), and extrapolating from the known to the vague, I've developed what I think is a reasonably-plausible adaptation.
This 1-gallon adaptation bypasses the corn-grit cereal mash with flaked corn and employs a 60-minute boil, rather than 120 minutes. The caramel malt that I chose was due to its middle-of-the-road quality, while the hops and yeast seem to be the best compromise between what was described and what is available. Northern Brewer is probably not exactly the right bittering hop, but it seems to be the closest that I can find to "California Gray." I chose Hallertau rather than Saaz as an aroma hop because I believe that the Germans who were doing the brewing would have used this Bavarian variety.
Based on the statistics, this adaptation seems to fit the BJCP guidelines fairly well; not perfectly, by any means, but to the point where the average home-brewer in 2016 can give it a go.
Anyway, here it is:
Kentucky Common Ale
TasunkaWitko's Adaptation
1 Gallon, All-Grain
OG - 1.050
FG - 1.012
ABV - 5.07%
IBUs - 27.21
Grain percentages:
60% 6-Row Pale Malt
37% Corn Grits
1.75% Black Malt
1.25% Caramel Malt
Based on 10-gallon adaptation, 1 gallon contains 1.825 pounds total grains = 29.2 ounces
Available information converted to 1 gallon:
17.52 ounces = 1.095 pounds 6-Row Pale Malt
10.8 ounces = 0.675 pounds Flaked Corn
0.5 ounces = 0.031 pounds Black Malt
0.4 ounces = 0.025 pounds Caramel/Crystal 60 Malt
Mash - 156 to 158 degrees
60-minute boil
Hops:
Northern Brewer - 1.4 grams = 0.05 ounces @ 60 minutes
Northern Brewer - 2.8 grams = 0.1 ounces @ 45 minutes
Cluster - 2.1 grams = 0.075 ounces @ 15 minutes
Hallertau - 1.4 grams = 0.05 ounces @ Flameout
Irish Moss - 2.5 grams = 0.09 ounces = 1/2 teaspoon @ 15 minutes
Yeast - Safale US-05 - 1/2 package = 5.5g
Sources:
http://www.bjcp.org/docs/NHC2014-kycommon-handout.pdf
http://bjcp.org/docs/2015_Guidelines_Beer.pdf - pg 55
http://www.seriouseats.com/2014/05/...e-saaz-fuggle-cascade-citra-beer-flavors.html
http://brooklynbrewshop.com/themash/hop-of-the-month-northern-brewer/