use a wrist sling, use an open hand grip, and let the bow fall until it hits the target then grab. Bow isn't going anywhere because of wrist sling.
If you have a good archery shop go there and have someone watch what you are doing sometimes the only way to fix something is to have a watcher help. A good shop most likely wont charge to help. Go when it is slow there.
Bill Winke uses those brown cotton gloves when shooting as they are slick to hold the bow with which will help eliminate torque. Uses them for that reason.
I have had a similar problem and turned out I was left eye dominant. I am a right handed shooter, so my arrows kept going right. I keep my left eye closed and my arrows are back on target.
Overall sounds like you might be gripping the bow a little much or too tight. Everything should be loose. Then it also sounds like you are too anxious to see where the arrow went and torque the bow literally as soon as you release. At this point it sounds like it might involuntary as you said you have been doing it since you started shooting 3 bows ago. I just started back up shooting and re-trained myself to shoot with both eyes open and can clearly see the arrow all the way to the target without moving the bow. Perhaps trying that and consciously thinking to not move till you hear the arrow hit.
I was having same problem with new bow. For me it was just playing around with where the grip seated in my palm. Also i cant have any closing of my hand whatsoever. Not even index finger tip to thumb. Totally open. Thats what solved mine.
Bows naturally want to torque to the right, so some of that may be normal. Are you shooting open handed or closed?
