I found a 1938 Newspaper Clipping:
https://www.newspapers.com/clip/27728870/1938-may-cookie-recipes/
It looks about the same but uses shortening, which may be more of a depression era cookie than using butter. It also includes an egg and 1 Tbs. milk. It doesn't say to double sift.
They bake at 400F for 15 minutes.
I'd guess that the original cookies used bleached flour, as that was what was available?
It's been a while since I baked sugar cookies, but I recall that those with Crisco spread less than those with butter. I also started rolling out the dough to the thickness I wanted BEFORE refrigerating, and refrigerating it on parchment on a cookie sheet. That way, the dough is colder. You could even cut out the cookies directly on the sheet, remove the excess dough from around them, and bake them directly. Any leftover dough could be rolled out, briefly refrigerated, then repeat.
All of this is to make your life easier, Italian Cook, when you use your leverage to get Aerogarden research....