I had the same problem you described- for 20 years of trad shooting I would end up shooting at the vital "zone" instead of a spot. I could easily pick a spot on 3-D, bales in my yard, stump shooting etc. For Pete's sake, I can hit golf balls at 18-20 yds.!
But every time I went to shoot at a deer-even after I "picked a spot"- by the time the arrow was at anchor I was looking at the entire "zone" or shoulder. The only time this would happen was on a deer. There was no way to practice it- it was situational.
I talked to Jay Kidwell about this- he is a sports psychologist. I know other pro/olympian athletes who likewise affirmed what I was exploring. The point being: this is a brain issue. It even has a name for my actual issue, "stimulus confusion." You can not practice your way out of it by shooting 100s of arrows. It is NOT a physical or "just concentrate" more issue. It is an actual "way" that your brain is processing information.
(Read that again- it is a "way" your brain processes info- physical training will NOT change it!)
You should read his book, but simply: I started year-round practice by shooting at a small round sticker (a button if you like). I put the sticker on everything (even my 3-D deer). In time, I periodically remove the sticker but "visualize" the sticker on the object I want to hit. In Jay's case, he carries around an actual "button" that he touches and handles throughout the week. When it comes time to shoot- he visualizes the button.
This trains your brain that no matter the target- you are shooting at the same thing. So, my brain started focusing on the same thing to be hit every time-a small round sticker (mine is black and about 1" dia- I may try orange this year).
Now you still have to practice- but your practice becomes as much a mental/brain training as a physical training. I am now working with the "way" my brain works. When a deer arrives- part of the "instinct" is now to "see" your "button" on the deer. And you shoot at the "button" not a deer! Believe me- it worked.
It made a HUGE difference for me when I apply it as a regular regimen of my practice.
I get sloppy in it sometimes because my confidence goes back up and I just like flinging arrows. (I noticed it last year on deer a couple of times). I then have to go back to the disciplined routine of practicing my "brain".
I am carrying on here- sorry- but one thing I notice is that few archers talk about these types of issues, while the world class athletes I know study this as much as physical technique. 30 years ago top athletes just began to think about nutrition and sleep cycles for training- they do now. Likewise, 20 years ago athletes rarely trained themselves mentally- they do now. I have a daughter that is nationally ranked Div. 1 athlete- she gets all this other training as much as she gets the physical.
Target panic, shooting over deer, etc. is all this mental stuff. It will take your shooting to a new level if you study and practice it.
Good luck