If they're tangier than you'd like that would be due to the acidity of the cream of tartar. While most recipes for Snickerdoodles do in fact us cream of tartar and baking soda for a homemade form of baking powder (most likely due to the fact that snickerdoodles are fairly "old"-style cookie), a few I looked at are using baking powder and no cream of tartar.
Here are a few things to know and a suggestion:
Acidic doughs do not spread easily and do not brown easily. Using the combination of cream of tartar in the 2:1 ratio w/ baking soda for leavening not only causes them to puff but with the higher acidic ratio it is also likely to help in keeping them more "cakey" and prevent them from browning as much.
You could try cutting back the cream of tartar slightly and seeing if that helps (possible drawback could be the soda making a more pronounced bitter soapy taste if there isn't enough acidity).
Or
Replace the cream of tartar and baking soda with baking powder. Baking powder by volume isn't as powerful as baking soda because of the fact it contains soda, two dry acids, and cornstarch. 1 teaspoon of baking powder will leaven 1 cup of flour (vs. 1/4 teaspoon of baking soda to leaven a cup of flour). If your recipe calls for 2 cups of flour then use 2 teaspoons of baking powder and cut out the cream of tartar and baking soda.
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!
Best Answer
From a food science point of view, in terms of the quality of flavor and the texture of the cookies, there is little reason to choose slicing over squashing; both will give very similar outcomes.
You may find the aesthetics or appearance of the cookies will be slightly different with the two methods. The sliced cookies will be more regular, especially if you cut them with dental floss; they will be quite round and even edged. The squashed cookies will be more irregular at the edges and perhaps show more texture on top.