Amie,
To the best of my knowledge, no one on this forum has attempted to reverse engineer and clone a Pizza Hut hand-tossed dough. But one thing I can tell you is that the dough that PH starts out with to make a hand-tossed dough is frozen. I know that from the PH ingredients list for the hand-tossed dough, at
http://www.pizzahut.com/files/pdf/ph_ingredients.pdf. However, converting a frozen dough to a fresh dough version is not something that can be done with ease. It can take a lot of experimentation and there would be no guarantee that your son would eat the pizzas in the meantime. We also know the PH nutrition information for the hand-tossed pizzas, at
http://www.pizzahut.com/Files/PDF/UpdatedPHBrochure01.11.10.pdf, but it is difficult to reverse engineer and clone dough/pizzas from that information alone. There is also the matter of coming up with a suitable equivalent for the PH pizza sauce. Again, we know the ingredients and their order of predominance from the PH ingredients list for PH pizza sauce, but there are many possible sauces that might be made based on the ingredients list, without any assurance that you will get close to a real PH sauce or that your son will eat pizzas with the sauce. It is likely that the cheeses you use will be better, with fewer additives and chemicals, than the cheeses that PH uses. So, I would be less concerned about the cheeses at this point.
Looking at the ingredients list for the PH hand-tossed dough, it seems to be similar to the ingredients used to make a Papa John's pizza or a Domino's pizza. I don't remember ever eating a PH hand-tossed style pizza, but the PH nutrition information seems to suggest that the crust is thinner than a Papa John's crust. I have had a lot of experience with PJ style pizzas and know how to manipulate the ingredients and quantities, including thickness, to achieve most objectives. I work with baker's percents almost exclusively, but as Bob mentioned there are tools that can be used to convert weights to volumes. The tool I use is the Mass-Volume Conversion Calculator at
http://tools.foodsim.com/. As an engineer, you shouldn't have a problem using that tool. However, to the extent that you achieve results that suggest that you are winning the battle, you will want to get a decent digital scale. As best I can tell, your Cuisinart mixer should be usable to mix the dough.
If you'd like, I should be able to come up with a PJ clone dough that should yield a finished crust that is thinner than what I believe PJ uses for its own pizzas and that may be closer to what PH uses. I recommend that a good bread flour be used, preferably the King Arthur brand of bread flour, which is the flour that I usually use for the PJ clone doughs/pizzas.
A point to keep in mind is that both PH and PJs use pizza screens to bake their pizzas. For a large pizza (they are 14" at both PH and PJ), you would want to use a pizza screen that is at least 14" in diameter. Pizza screens are sold by most restaurant supply stores and also online. You can see what a pizza screen looks like at
http://www.wasserstrom.com/restaurant-supplies-equipment/Product_119991. If you do a Google search, you will find many many other places that sell pizza screens.
It might also help to know what kind of PH pizza your son likes (e.g., cheese, pepperoni, etc.)
Let me know if you would like me to proceed. In the meantime, you might want to take a look at some of the photos and read a few posts in the PJ clone thread at
http://www.pizzamaking.com/forum/index.php/topic,6758.0.html. Doing that might tell you if a PJ type of pizza is something that your son might eat. You might also take a look at the thread at
http://www.pizzamaking.com/forum/index.php/topic,1707.0.html. I mention that thread because I made "thin" versions of another member's Papa John's style pizzas. You might even discover that one of the recipes at the abovereferenced threads will work as is for your purposes. I wouldn't expect any pizza on this forum to look like the photo you posted. Even PH's pizzas from their own stores are unlikely to look like the professional photos at the PH website.
Peter