On my experience...
This was a very large goat, probably over 150 pounds. It took two of us to wrestle him to the ground. I stepped back because I didn't want to participate in the kill, but his son took my place and held him. My friend thanked the goat, said a prayer, repeated God is Great three times, and quietly slit. Don't know if that is how it usually done, but that is how he did it.
He is very skilled as I said, but I believe that is the key to humane Halaal slaughter. One reason he doesn't want others doing it (besides ensuring correct bleed out) is because he doesn't want the animal overly stressed by an improper slit, whether they are Muslim or not.
If I was going to slit something as large as this goat, I would stun, but if I had more confidence, I might not. I'm not going to pass judgment on others' choices either way.
BTW, if you are going to shoot a goat, don't shoot it between the eyes. That's about the thickest part of its skull and an invitation to a painful ordeal for both you and the goat. You shoot it behind the head at a somewhat downward slant, between the ears.