Congratulations on the successful outcome. And getting such good results on the first try makes it even more rewarding. Did you take any photos? If not, did your pizza look like Giovanni's?
BTW, there is no reason why you can't use your stand mixer to make Giovanni's dough. You may have to play around with the process a bit, but, from what I can tell, a stand mixer is what most home pizza makers use.
You may also find that you don't need to use the dough freezing step for your second dough recipe. Giovanni uses it in his recipe to cool the dough down faster before putting it into the refrigerator compartment to spend the next 24 hours or so. I would guess that using the dough freezing step for your second dough neither hurts nor helps the dough that much over a 20-minute time frame, and that the bulk of the fermentation and flavor development takes place over the 4 hour rise period. You might want to run a test sometime without the freezing step to see if you notice a difference.
I'm not surprised that you got better results than with your bread machine. After playing around on several occasions with a bread machine, I concluded that a bread machine does a better job at making bread dough than pizza dough because of the programmed heat/knead cycle, which is more attuned to bread dough production. You might be able to get around some of the programming to make a good pizza dough, but it takes a lot of fiddling around with water temperature and knead times to do so.