I had that problem last year and picked a couple of four gallon buckets off when they were maybe golf ball sized from two trees. I thinned them a lot more than a fist apart and still had plenty. The ones left get bigger if you thin them earlier. Your bracing should help a lot, but those peaches get really heavy and peach tree limbs are pretty brittle. Even with the bracing it might be worth picking off some of the imperfect ones, the ones with bug bites or the ones that are knotted. You 're going to have more peaches than you know what to do with. That's a nice problem.
I did not get any peaches this year, our spring was warm so they bloomed early, then a frost got them. Same thing happened with plums. But I still had a peach tree branch break. My guess is that a raccoon, possum, or groundhog climbed out on the end of a limb for some reason and the limb snapped. My fantasy is that it was trying to get away from a coyote and the coyote was waiting on the ground when the branch broke.