Much of rules lawyering and elements of AP (and certainly perfectionism) are about control. The lack of it creates anxiety and fear about the consequences of poor decisions or not having the right answer. One solution is to place yourself squarely in situations where you don't have or you abdicate control.

When you play games, make choices that are random. I would even go so far as to suggest using dice to make your choices for you (e.g. if you have 4 choices of actions, roll a die to determine which action you choose). Or simply make a quick choice without thinking about it (i.e. choose actions in order on the reference sheet, choose an action that's alphabetical, etc.). You need to directly face not being in control and get more comfortable with the consequences - which are simply that you might lose. If neither of these appeals, talk out the options you have with another player and let them give you input and be willing to go with that.

You can certainly also impose a time limit on yourself. But if you are still engaging in the same way during your turn, the time limit is more likely to just amp up your anxiety. Sure, it will guarantee that the next players gets their turn, but each time it comes around to your turn I think your anxiety will just be higher unless you interrupt the way you approach your turn within the set time limit, which will also make it more uncomfortable for the other players.

The same goes for rules lawyering. As others have pointed out, let someone else make the call, ideally the owner of the game. But you need to explicitly acknowledge you are deferring to someone else. And you should not have access to the rule book.

Post game reflection is also important. Talking about how the game went, reflecting on the fact that you can still have fun and engage without the need for perfection, and realizing that your actions did not have the detrimental impact your inner voice is telling you it would have will go a long way in unlearning some of the habits you have.

Meditation can also be quite helpful. I'm not suggesting that you go in a corner and chant "ohm." But in the moments where you feel anxious, just take 30 seconds to pay attention to your breathing, tension in your body, etc. Not only will it relax you, but being present in the moment can reinforce that you can be focusing on the people around you and the fun, and not on controlling the outcome of a game.