I spaced my trees at the farm at 18’ between the trees within the rows and 25’ between rows. At the house I spaced my trees at 20’ on a diamond. You can get a few more trees per the amount of space you are filling with a diamond planting vs. planting on squares.
Really though I’ve learned there is no “correct” answer when it comes to peach tree spacing. I’ve read lots of recommendations from various extension materials, and there is a lot of variability in the spacing recommendations, even with the same tree training method (i.e. open vase, quad, etc.). I even asked peach guru Jerry Frecon on another forum once about optimum spacing and he didn’t give me a definitive answer.
Here, all the commercial growers space their peach trees a little different. I probably give more space than just about anybody though. The reason why is that when I just had peach trees at the house on 20’ spacing, they were wanting to grow into each other. I have to keep mature trees pruned back quite a bit just to get a riding mower between them (My riding mower has a small roll bar which sticks up.) I knew how I train my trees that I would have problems getting a tractor down the rows if I spaced them much tighter than 25’ between the rows. In fact, I have to prune some of the trees a little after the growing season to be able to get the tractor down the rows without hitting branches.
It really depends on the vigor of the trees and how spreading you train them. It does control their size to some degree when you pack them tight. But if I tried to pack them tight, it would a nightmare to try to keep them from growing into each other.
I probably wouldn’t recommend something as tight as the 10’ spacing you mentioned (for normal open vase trees) but there are people on the forum who space them even tighter. I think it gets to the point though where you have to keep pruning so much wood to keep the trees in their space, that yield can go down dramatically, because you always have to keep pruning off about all of the new productive wood.
Btw, I liked the history and pic you shared about VA mines. Very interesting.