Z, a few thoughts.
Until you get a wood fired oven and start making Neapolitan pizza, always grate the cheese.
As I think you're figuring out, a digital scale is critical. If you want any kind of consistency, you should purchase one before your next batch of dough. If you want to put in some time researching a good one, that's great, but, imo, it's way better to have a cheap Walmart one than no scale at all. Once you get a digital scale, come back and we'll have a much better recipe for you.
Are your containers round? A round container goes a long way in helping you to shape a round pizza. Practice also helps. Here's a good video on stretching (ignore the rolling pin stuff):
Make an extra sacrificial dough ball just to practice stretching with and stretch it as far as you possibly can.
How hot does your oven get? Are you pre-heating the stone as high as your oven will go? How long are you pre-heating the stone for? Does this oven have a broiler in the main compartment?
"Off the charts" pizza needs consistently measured ingredients as well as consistently fermented dough. You might run across dough recipes where the dough is made one day and either used that day or 3 days later, but an "off the chart" recipe will have a much smaller window of usability. You want to pick a time frame that works for your schedule, preferably 2 or 3 days, use enough yeast so the dough doubles in that time frame, and stick to that schedule every time. In other words, develop a 2 day dough and always, if possible, make it 2 days in advance.