As promised, I have set forth below the formulation that is intended to be a mash-up of the Bisquick Original Pancake and Baking Mix and the Buttermilk Bisquick biscuit mix, as further modified through the use of a "goody bag" to produce what hopefully will be a functional pizza dough.
Here are the steps to follow:
Add 212 grams/7.48 ounces of the Bisquick Original Pancake and Baking Mix to a bowl
Add 160.5 grams/5.66 ounces of King Arthur bread flour (KABF)
Add 1.11 grams/0.04 ounces of the Clabber Girl baking powder; this comes to a bit over 1/4 t.
Add 0.80 grams/0.028 ounces salt; this comes to 1/8 t.; you will have to adjust if you decide to use a Kosher salt
Add 8.67 grams/0.31 ounces dried buttermilk powder; this comes to 1 1/2 t.
Add 2.41 grams/0.09 ounces dried whole egg; this comes to 1 1/2 t.
Add 0.85 grams/0.03 ounces soy flour; this comes to a bit less than 1/2 t.
Add 2.26 grams/0.08 ounces of IDY; this comes to 3/4 t.
Using a pastry cutter or its equivalent, cut 12.84 grams/0.45 ounces of partially hydrogenated soybean and/or cottonseed oil into the dry ingredients (but see instructions/notes below)
Total weight of "goody bag" contents = 401.04 grams/14.16 ounces
There are two components of the water:
Water 1: 94.18 grams/3.32 ounces (this is in relation to the presumed cake flour in the Bisquick Original Pancake and Baking Mix; hydration = 55%)
Water 2: 99.49 grams/3.51 ounces (this is in relation to the KABF; hydration = 62%)
Total weight of water: 193.67 grams/6.83 ounces
Grand total weight of the "goody bag" and the water = 594.71 grams/20.98 ounces (for one 16" pizza with a corresponding thickness factor of 0.104)
As noted above, one of the new ingredients for the "goody bag" is the partially hydrogenated soybean and cottonseed oil. As previously mentioned, you are not going to find such a product in the supermarkets on a standalone basis. In fact, the entire fat scene in supermarkets has changed dramatically over the past several years, with a concerted effort to reduce or eliminate hydrogenated fats, and particularly the dreaded trans fats that are a byproduct of hydrogenation of oils. The "old" Crisco would have been a good choice for our purposes but the "new and improved" Crisco has been dramatically changed (with different oils and combination of full and partial hydrogenation) and no longer meets the fat profile (total fat/sat fat) for our application. Butter and lard could be used in a pinch but they do not meet the desired fat profile either (too much saturated fats).
The closest match that I could find is a basic, solid, stick (not soft or tub or liquid or butter/margarine blends) supermarket margarine. Of the brands that I checked out for our application, the Imperial (original) brand of margarine seems to offer the best match. Unfortunately, margarines these days, including the Imperial brand, include many other ingredients, such as whey, some liquid oils, colors, flavors, and preservatives and the like. They also include water and salt. These ingredients may not materially affect the outcome of our project but that is something we will not know until the results are in, and maybe not even then. For the Imperial margarine, I suggest using 14.98 grams/0.53 ounces. That comes to 1/2 T. (or the mid-point of the tablespoon markings on the paper wrapper). That value also compensates for the fact that margarine contains around 17% water. For the amounts used, that is not likely to be a problem with final hydration. As you discovered before, you had to add more water than I calculated. I suspect the same may occur with the above formulation.
Happy Mother's Day.