Welcome to the forum.
There were several things left unsaid in your post, but I will do my best to try to address what I believe were some of the underlying causes of some of the problems you identified.
First, your recipe uses both all-purpose flour and bread flour to make a Neapolitan-style pizza dough. A classic Neapolitan pizza dough is made from Italian 00 flour, which is quite different from the two flours you used--in terms of protein content, hydration (the absorption of water by the flour), and several other differentiating characteristics. Since you used volume measurements instead of weights, it's a bit difficult to tell whether your proportions of flours and water are correct. I weighed three cups of flour and a cup of water on my digital scale and I calculated that your hydration (the weight of water relative to the weights of flours) is around 52%. That would be OK if you were using 00 flour (it would still be a bit on the low side) but it isn't high enough for the two flours you used. I estimate that you may need about 1/8-1/4 cup more water. Otherwise, you can expect to have the high degree of elasticity ("memory") you experienced, as well as a somewhat reduced rate of fermentation.
Second, unless your KitchenAid mixer is different from most such mixers that I am aware of, your kneading of the dough was far too aggressive. You kneaded your dough too much and for too long and at too high a speed. In Italy, long knead times are used, but the flours are different, the kneading is actually quite gentle, and the machines used for kneading are different. The procedure I would recommend in your case with your particular flours and other ingredients is as follows: combine the two flours in a bowl; dissolve the yeast (I assume it is active dry yeast, or ADY) in a few tablespoons of warm water (at about 105-115 degrees F) and set aside for about 10 minutes to proof; place the rest of the water (on the cool side) in the KitchenAid mixing bowl and dissolve the salt in it (as by whisking it with a wire whisk or a spoon); add the yeast/water mixture to the bowl, stir, and gradually add the flour while the mixer is operating at "stir" or 1 speed. At this stage, the paddle attachment or dough hook can be used. Once a good part of the flour has been added, use only the dough hook and continue to add the flour and knead until everything comes together in a rough ball; continue kneading until the dough takes the shape of a smooth, elastic ball. This should happen in about 7-8 minutes total, at about 2-3 speed. Ideally, the finished dough ball should be a bit tacky, and not wet or dry. Since you are using volume measurements, which can be imprecise, you may find it necessary to add more flour and/or water to get the desired final condition of the dough ball. Don't be afraid to stop the mixer and to inspect the dough, remove it from the dough hook if it rides up on the hook, or to do a little bit of hand kneading. Home KitchenAid mixers are not particularly good at these kinds of operations (unless you have one of the special dough hooks that KitchenAid produces). I suspect the doughy character of your finished crust was due to overkneading, which quite likely resulted in a more bread-like character to the crust.
Third, you didn't indicate whether the 24-hour rise period was at room temperature or in the refrigerator. If it was at room temperature, as is very typical in Italy, 24 hours would be excessive, and especially for the amount of yeast you used (a 1/4-ounce package). I don't know where you are located or the temperature of your kitchen at this time of year, but if you used a room-temperature rise, then you could have used as little as 1/8-1/4 teaspoon yeast. Using a 1/4-ounce packet of yeast would have resulted in the dough ballooning at room temperature--by two to three times. If you meant to say that the 24-hour rise was in the refrigerator, even then you would have seen a significant volume expansion in the dough. But if your refrigerator was really on the cool side (say, around 35 degrees F), then it would have been possible that your dough didn't rise much while in the refrigerator. But if you used all warm water and 1/4-ounce of yeast, then it's hard to imagine that the dough didn't rise much while in the refrigerator.
Fourth, I estimate that the amount of salt you used was about 3.8% (by weight of the two flours). That's high even for a classic Neapolitan dough, which tends to be higher than with other doughs. But it excessive for your recipe. Excessive salt will toughen the gluten strands in the dough and slow the rate of fermentation of the dough. This can yield a tough dough that doesn't rise to the desired level and is hard to handle. I would reduce the amount of salt to about 2.4%, which would be a bit less than 2 teaspoons (if my flour weight measurements were correct).
Fifth, you might consider adding a bit of olive oil to your recipe. That will help the extensibility of your dough (its stretchiness), especially if you make the other changes recommended above. I would use about 1-2% (by weight of the two flours). That would be about 1-2 teaspoons. It can be added to the mixer bowl just after the flours are added and combined with the rest of the ingredients.
Sixth, if you placed the corn meal on a preheated stone, it will burn as you indicated. Should you choose to use corn meal, it should be placed on a pizza peel and be used as a dusting agent to help release the dough into the oven onto the preheated pizza stone. But you don't have to use corn meal. You can also use plain ordinary flour. You also shouldn't put a cold stone in the oven with the pizza on it. The pizza should be deposited onto a preheated stone.
Seventh, I believe there is a lot you can do to improve your sauce. There are many threads on this forum that deal with that topic far better than I can do on this post. I will mention, however, that classic Neapolitan pizzas use San Marzano tomatoes. There are several threads on this post that also address that subtopic. If you use the site's search feature you will find a lot of posts that should help you achieve a better sauce.
I think if you give the above suggestions a try, your children will be coming around for five and six helpings
. If I forgot anything, or if you would like to submit further information for review in light of my comments above, please feel free to do so.