It may be because of the type of yeast being used. Quick-cooking bread machines (1 hour cycle) typically requires "instant" yeast which rises much faster. Standard-cooking bread machines (2-3 hour cycle) need regular yeast, which is active longer. It sounds like you're using instant yeast in a standard recipe; thus the yeast stops working before the bread machine gets to the second rise cycle. Under-cooking may be because the resultant dough is denser than the machine expects, thus doesn't heat through in time.
Unfortunately the trade names for "Regular Active Dry" yeast and "Instant Dry" yeast can be very confusing.
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
If the edges burn and the center is undone, it means the heat didn't have enough time to reach the relatively cool center before the edge was too hot. The temperature gradient depends on the amount of heat from your oven and the size of your cookie - and to some degree on the thermal properties of your cookie sheet.
You have mentioned the two "usual suspects" in your question:
Oven temperature and convection.
If those two don't help, look into the type of cookie sheet and the temperature of your dough when it's put in the oven - chilled dough will behave differently from room temperature dough, for example.