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!
The cookies will set (take on their final texture) about by 20 - 30 minutes out of the oven. Coming directly out of the oven, cookies will absolutely be soft and squishable; which is why you should wait a few minutes before moving them off the baking sheet and onto a cooling rack (you can cheat this time if your cookies are all on a sheet of parchment paper, and you move the parchment paper as a whole).
Best Answer
I don't believe you will be satisfied with any cookies you roll out and cut from this dough. That said, there are three options that may allow the dough to find a tasty future.
Make a 'Mega Cookie': roll the dough out and fit it onto a pizza tin and bake. This can be decorated as one large cookie/pizza.
Make 'Brownies': work the dough into an 8"x8" or 9"x13" pan and bake.
'Cupcakes': scoop a spoonful of dough into each compartment of muffin tin and bake.
Of course you will have to watch to get them done enough as the standard bake time probably won't apply.
If your recipe doesn't include eggs (or you are not concerned with the risk that raw eggs may pose) adding it to homemade ice cream would be a fourth option.
Good luck.