Preheat while doing other things. That's not a step that should take any effective time.
Don't measure so obsessively. Unless these need to be immaculate cookies, just accept a little variety. Scoop roughly with a spoon, or just your hands, and form into balls with your hands if necessary. If you desperately want precision, you could use a cookie dough scoop. But 56±3g sounds kind of over the top to me. Given that you said this is the main time sink, I'd suggest loosening up a bit.
Are you filling your cookie sheets fully? Do they fill your oven? Following a recipe's instructions to the letter, baking only 9 per sheet, is obviously the wrong thing to do if your cookies or baking sheets aren't the same sizes as those in the recipe. Note also that if you have many cookies per sheet, you can often fit more by tiling in triangles instead of squares.
And finally, reconsider your recipe. I'm sure this one is great, but keep in mind that most standard chocolate chip cookie recipes bake at 350F or 375F, and times more in the 8-12 minute range. If your recipe gives you exactly the cookies you want, and others don't, then stick with it, but if you're unnecessarily sticking to a recipe, try something else.
Edit: one more thought! Chilling the dough is probably important to your recipe, but you could measure/scoop while it's warmer and easier to work with, then chill in balls, and do the final forming once chilled.
And another, having seen your comment: given that you increased the baking time upon filling up the oven more, and are using insulated pans, you might actually want to increase the temperature to 350-375F and see if you can get back down to the 15-18 minute baking time. They may end up closer to the originally-intended consistency!
Sounds an like you may just need more flour. That recipe has more fat per flour than common cookie recipes - for example, the canonical chocolate chip cookie recipe has 10 oz of flour for 1 cup of fat, while yours is only about 8 oz flour per cup of fat. So I'd definitely expect the dough to be on the soft side to begin with, and since the fat softens at it warms up, as you've seen, it just gets worse.
If your kitchen is on the warm side, it's possible that you'll also need to chill in the freezer instead of the fridge, but I'd certainly start with more flour (or less fat).
Best Answer
My own sugar cookie recipe is quite dry as well. It cracks along the edges when pressed or rolled and is easily "broken".
I've never experienced a problem with the dough being so dry it doesn't take to cookie cutters, but if your dough is literally falling apart you may want to just spritz (or in the absence of a kitchen water spray bottle, sprinkle with your finger tips) cold water on it. (Like adding water to pie dough) Give it one sprinkle/spritz and kneed it in. Repeat until it just stops breaking. Don't go overboard and make it gooey.
I'd use water over oil or milk because it's the least likely to change the structure of your cookie in the baking process. Such minuscule amounts of water shouldn't yield a detectable change in the end product.
If this is a consistent problem with the recipe, in the future I'd decrease the flour by a tablespoon or two and see if that helps.