TL;DR: Play Payday 2
First of all, I know it's "shoulder fire" and not hipfire, but everyone will understand by calling it hipfire.
Yes, by playing Payday 2 I've learnt A LOT to shot from the shoulder. In that game you also don't have any type of crosshair (this was for me the biggest problem, not knowing exactly the center of the screen), and a lot of times you face enemies at point blank, so by instinct I started shooting them from the shoulder and in the 20 hours approx I've spent on that game in the last week, I've became way better in this mechanic. I just don't ADS at all when I'm below 20 meters, and with pistols I'm still getting more than 70 % accuracy (in Payday). And back to Tarkov, I've been playing Factory raids today and got plenty of shoulder shots, while previously I couldn't even think about that. Not only I can shot more easily, but also I've become more confident at it.
What I suggest: If you like Payday, give it a try this way, take only pistols/high mobility weapons and try to not ads. If you need so, attach a laser point to it and go into a heist. A shotgun can also help at the beginning. It's important also to mention that the best way is to try only giving headshots, as in both games are critical to kill players/bots.
I know a lot of people say that you can try same similar at Factory with a lot of bots, but in Tarkov one becomes more aware from the health and other statuses of the pmc, while on Payday you can just join a low difficulty heist and don't worry at all of dying, so you focus more on landing those headshots.
Maybe it was just me, but I think you can improve on a similar way by trying this.
(Sorry for my bad English)