I think the US Cavalry was right. Stirrup strap should hang straight down. With my saddles (including English), ball of foot in the stirrup, that puts the heel in a vertical line with my belt buckle - like the dressage rider shown above, or this one:
I will sometimes ride with my heels further forward, for my own reasons:
However, in my experience, it makes cueing your horse a challenge. My calf is either on or barely behind the girth, and it just means more pressure is needed for her to feel me. I normally will bring my heels back a few inches to cue when I'm riding that way.
I'm not an instructor, but a saddle is designed to have your rump in the deepest part and the stirrup straps or fender handing straight down. That results in gravity being your friend instead of your foe. In most saddles, that should put your calf & heel just behind the girth. With my Aussie-style saddle, it normally puts my leg here:
I ride with both, but if I could only choose one, it would be calf/heel a little behind the girth, with the stirrup strap hanging vertical.