Do you have any nerve damage in relevant parts of your body? Might be once you zero in on perfect technique, you're using areas that are niggling away at something that was just waiting to flare up. Just a thought. Only you'd know for sure. I've done a lot of very nasty things to my neck and back over the years and I find a perfect technique for me is one that aggravates none of it... I could sling all afternoon, versus two hours of shifting plants around which will render me a basket case for two hours afterwards. After repeated injury the body learns pretty well how to take you offline before any real damage is actually done.
I find anything that leads to a sore arm or hand means I have been trying to sling on a bad back day and as such am relying too much on the flick of my arm than the pivot of my hips or set of my shoulders.
You may also find that the adrenal reward of doing a good job for a while will tend to make you jumpier, faster and more jerky in your movements. It sounds strange, but try having a strong chamomile tea or half an hour of quietly breathing and looking around the area before starting. Being outside the mind is a good way to control the body properly. I actually find my accuracy (worryingly?) increases after a beer or two. Smooth muscle relaxaton may be involved here. Tip - don't sling after having any more to drink than would mean you couldn't drive legally anymore.
Overthinking has something to it, but then if the same logic was applied to sighting in a rifle, noone would ever do it. As it wouldn't ever work
Bit like saying "hey, youre paying too much attention to the road and your vehicle, knock it off!". I think the distinction here is the line between thought, and self doubt or second guessing.
The trick here is changing ONE variable and keeping a good idea of the last thing, and the current thing, you did. Thinking about and consciously adjusting technique is something almost all of us do, the times when we think we aren't it's because we've remembered the golden rule of pay attention to the tool, but think more about the outcome. Musicians do this all the time when they are learning to play, or trying new styles.
You cannot change the target, it is indisputable. So focus on hitting it. If you're 10 degrees out, adjust your action by one degree the other way. And so on. The body and the motion in slinging is not a series of straight levers despite impressions, it is one fluid curve leading to another, to another, to a smooth trajectory. It is a business entirely based on tangents and as such slight differences at the start have profound differences on the outcome. I get what people mean when they break their technique up into footing, hips, facing, turning-away, all that... but to me it's a bit like treating your wheels as distinct from your steering rack from the rest of the car.. it all has to work together, or none of it is going to get much done at all.
I found it really helpful to be hard on myself as far as targets go... if you say "happy to hit that 10m square" then you give yourself 30 metres of actual space to play with... but aim for a specific knothole on an old post and whilst you might not hit it as often, missing a one inch target at 80m, by a foot, is a bloody good show. Missing a barn by a paddock is not very fulfilling.
I find accuracy on level ground much easier than my usual sloping terrain, it's like all the mental programming on board to compensate for rises here and high winds there suddenly make a mockery of the simple business of trajectories.
I also found ith elps to work on high accuracy first... ie, hitting the top of a phone pole rather than the base (I don't know why, and this may differ for others). Once you can hit the right "midpoint" of the arc en route to the target, the rest of the shot takes care of itself. I would have better luck hunting birds or bats with a sling than I would rabbits, anyway.