Ok, so you want to know why culling my park deer is different, and why I have made the personal decision as to why I think my park headshots are ethical, despite my reservations about wild headshots? Note: every shot for every stalker is a personal decision. No one else can make the decision for you.
I don't expect to change your opinion, just as you are unlikely to change my opinion on neck shots, but I do hope it'll make you a bit less judgemental.
Firstly, I am under no pressure. I haven't driven 200 miles to my ground, and this is the only opportunity that presents itself at the end of a blank day (which I think is probably the reason why most messed-up head shots are taken). In the park, if the perfect shot doesn't present itself, I can just walk away. Go and do something else for an hour or two. The deer will still be there later.
Secondly, it is easy for me to take whatever aids to accuracy I might need into the park, as it's not far to carry stuff. Sticks, tripod, whatever. There's no risk of having left something in the pickup and not having it available when I need it.
Thirdly, choice of rifle. Much as I love my hard-hitting .270, I know it isn't my most accurate rifle. It's great for chest shooting where there's more margin for error, and I need the additional clout to punch through ribs etc, but for the headshots in the park I can use a smaller calibre more accurate rifle for headshots, as I'm not going to be chest shooting anything.
Thirdly, bullet choice. I use a lightweight (58 grain) very fast (almost 4000 fps) extremely destructive bullet. It would be eminently unsuitable for chest shooting, but the very flat trajectory (when compared to a heavier, slower, bigger calibre bullet) gives me the accuracy I need, and the destructive design gives a small, but nonetheless significant, margin for error.
Fourthly, range is limited to sensible distances by virtue of the fact that it's a small area, so there is zero temptation to take shots at extended ranges.
Fifthly, in the unlikely event that something goes wrong, there is zero risk of losing the animal. Follow up is immediate.
Sixthly, headshooting the deer I want causes considerably less stress to the rest of the herd (which, as someone who works with livestock, I'm sure you'll agree is a very important consideration).