Yes, it probably goes without saying, that there is no right or wrong way to make pizza! Though I'd contend that there are better and worse ways..
I think it's not so much a question of a recipe but rather that of a process that you have to work through to find the way that works for you, and that delivers a result that YOU are happy with. I'm amazed that I've ended up at 58% with Caputo pizzeria flour.. By many accounts that's too little, but still it seems to work out for me with 70, 150, and 210 seconds pizza (different Italian styles). I also undermix my dough, albeit in a spiral mixer and when I ball after an hour it's super smooth.
This one is really difficult to explain, but making pizza is also a chain of steps that you go though, and any deficiency in an earlier stage will make later stages more difficult, as well as it might cause even bigger problems later (the problems intensify). When you have a problem with the final product, then go back and examine your experience at each step, trying to figure out where it went wrong.
One of the problems when starting out at home making pizza is that you don't know how the dough should feel, if you would have been taught by someone you'd have that tactile sense that tells you when things are right. Lacking this all you can do is experiment, but I'd advice to hand mix a few doughs.. By all means use a KA, or other kitchen mixer to mix the components, and once it starts taking form thow it on the kitchen bench, or a stone or a table and start kneading it. Keep turning the dough 90 degrees, and pull it out and fold it back over itself. There are loads of methods and videos on youtube, hard to say which is better.. Many different ways lead to rome, but they'll all be slightly different!
With a couple of tries you'll start feeling when the dough is starting to dry up and going from sticky to tacky, I can only describe it as getting a skin on the outside. This is what the Italians call the punto di pasta, and it's the point where you stop kneading, let it rest for a while, and then form the balls. After that you can RT or CF it, I'm in the RT camp as I have a small fridge and no place for a dough tray, but also because this is the traditional Italian way.
I don't know American flours so I can't speculate what hydration you should use. But I'd contend that if you are having problems at 65%, then try 62% and see what happens. There is no absolute truth that 65% is better than 62%, in fact it also depends on how you make the dough, how you ferment it, etc, etc. It also very much depends on your oven and baking time, the one thing you don't want is a gummy or under baked crust. That is IMO meh, and not very digestible.
To the OP, if you really are serious about learning this, then please post photos (and/or videos) of your dough at the various stages, I'm sure that there are many here waiting to help you. Not the same as learning from a master, but this is a really great forum and a great place to learn!
Also if you go the folding route, then observe your dough very carefully. If you see that the fold did something good to your dough, keep doing it. Once it doesn't seem to improve, then stop! And if you continue to force it, you'll see how it starts to deteriorate, in that case stop immediately and say three Ave Maria (or similar)..
But it doesn't sound like you folded the dough too much.. Let's see what leaving a bulge in the middle, some edge stretching, and maybe some knuckle stretching of your dough brings. And please, post photos..
Also be aware that when you ball the dough you'd like to create a tension on the outside skin, but you don't really want any holes on the bottom.. If you start with the finished dough ball upside down you can close any obvious one with your fingers, but if too big they can lead to thin spots in your pizza.
To finish off, I thought your photos looked really nice, I'd be happy to tear into that pizza..!
