I have been experimenting with flours & recipes for use in my home oven, and have reached the same conclusion as you, after hoping that I could find a way to make high-temp dough recipes work in my low-temp oven without changing the ingredient list. I haven't totally given up this quest, but the addition of amendments goes a long way to improving home-oven recipes.
With my stone on the bottom of my gas oven, I can get deck temps of 660, which is admittedly slightly higher than what you mention here, but not high enough to make a difference, in my opinion. At this temp my pies cook in about 8 minutes.
My current recipe uses Caputo at 57% hydration, with 1.7% olive oil added after machine kneading is complete. This gives a pretty good pie with a crisp, brown crust, a fairly soft interior, and a great dough flavor and aroma. (To my mind, the most significant benefits of using Caputo is the flavor it lends to the dough itself.)
To me, the "toughness" factor is the hurdle I've been working to overcome in all of my doughs, Caputo or HG. This is manifest in two ways. One, tough crusts tend to pull up at their sides in the oven, and are unpleasantly chewy. Two, these features get even worse on cooling.
One of my benchmarks for a good pie, after how it tastes and behaves right out of the oven, is how it tastes and behaves the next day. To my mind, a really good pizza should be tender and tasty even when cold from the fridge or the counter the day after baking. My own pies rarely if ever get to this quality, but it is true of most of the pies I like from Pepe's or Modern. I live in Cambridge, and whenever we go to New Haven we bring many pies home to prolong the ecstasy as long as possible, since we only get down there a few times a year. We just leave the pies on the kitchen table, and the next day they are still delicious right out of the box, and reheat wonderfully.
My current thinking is that to keep crusts tender on the inside while cooked on the outside, high temps are ideal, since the exterior browns before the interior dries out. Dough conditioners can help to keep the interior moist and to promote browning, so that cooking times are minimized, but so far the difference between high temps and modified recipes is still present, and remains my holy grail.