How can I substitute dutch chocolate cocoa for flour and maintain proper recipe PH in this cookie recipe? I have an old family recipe for Chocolate chip cookies

2 ¼ cups flour
1 cup white sugar
½ cup brown sugar
1 tsp salt
1 tsp baking soda
2 eggs
1 cup shortening
1 tsp vanilla
Chocolate Chips as desired.
Add dry ingredients then wet ingredients to a large bowl, mix until well incorporated, seperate into golf ball sized dough balls, bake at 375°F for 8m15s

I want to make it into a chocolate chocolate chip cookie. I've followed advice from several online sources and just replaced about 1/4 of the flour with cocoa (so it's 1.5 cups flour , .75 cups cocoa). I've tried with both regular cocoa and dutch process and I really like the darker look of cookies that come out with the dutch process, however their texture isn't right. I have used this recipe and the flavors seem good, but I also want to get the texture right; the original recipe is very chewy, soft and moist, but the chocolate modification wound up much drier than I wanted.
After some research I found that the basic issue is that I've screwed up the PH of the recipe. I believe the fix involves substituting some or all baking soda for baking powder, but can't find a clear rule for how much. My guess would be since I'm effectively removing 1/4 of the acidic ingredients (flour, ph 6-6.8) and swapping them for ph neutral ingredients (dutch process cocoa), I should replace 1/4 of the baking soda with baking powder as well, but can't really find any information on how to go about replacing baking soda with baking powder or what ratio.
Edit: Upon more research I've also found that instead of modifying the baking soda I could just add some volume of cream of tartar, but I'm still not sure how to calculate this cost.
I doubt this is an acidity issue. Most flour is pretty neutral, the reason your cookies seem dry is that they are dryer. Cocoa powder is about 7% moisture, source doc here, whereas flour is about 14% moisture, see this site for details. Add to that cocoa powder is very fine, and likely more absorbent than the flour, and the fact that the dutching process makes the powder more absorbent. So the cocoa you add is dryer, and absorbs more moisture from the rest of the ingredients and you will need to add some in to replace it. 

Looking at the math .75 cups of flour is about 85 grams, 14% of 85g is 11.9, rounded up is 12g. Cocoa has about half the moisture, so you have lost about 6g of moisture in your recipe, which is just over a teaspoon, under ideal conditions. However, often when flour is stored it absorbs more moisture from the air as it is not kept airtight, so you could be losing more. A dry cookie dough will sometimes have trouble coming together, and be crumbly, which is something I would look for in your case. I would try adding a teaspoon of milk or water to your recipe and see if that creates the right consistency, and then add another if it still wants more.