That was a hell of a write up! Like sacountry said, pretty good for a CPA!!!
The following is all speculative.
@Big Fin I believe you were shooting over the goat the first couple shots because of the angle. I'm assuming your rangefinder has angle compensation, but you might not have had it turned on, or whomever was giving you the range was giving you the true distance instead of the TBR (true ballistic range).
I ran some quick math with my ballistic profile for my .338WM.
If I was shooting a level shot at 350 yards, I would need to dial up 5.3MOA.
If I increase the shot angle to 30 degree at 350 yards, I would dial up 2.9MOA.
For my rifle, a 2.4MOA off at 350 yards would mean I was shooting 8.4 inches high. I'm going to assume that's what was causing your shot to go over his back.
Gravity effects the bullet on horizonal distance instead of vertical distance. It's sort of confusing, but your rangefinder should be able to spit out a shoot to distance, or at least the angle you're shooting at so you can figure the math out! The good news is, those first 2 shots might have missed, but it wasn't due to shooter error. Don't beat yourself up over it! You punched your tag on a hell of a goat.
I cannot wait to see this episode!