Has anyone overcome this problem? Where would you go to interact with strangers–importantly where there’s an appropriate social context that permits interacting.
First: Work a job that is socially embedded. Restaurants, grocery stores, front desk retail, anything customer service related. Getting comfortable with people has a weird out-of-order solution where if your discomfort is visible, the interaction will sour; find something that forces a fix to the initial discomfort, like the jobs above. They'll act as a shim that'll let you bypass the initial anxiety.
Second: The emotions you wear on your face are what perpetuates a conversation. If you can find a reason--not act, not fake--to want to talk to someone, to learn about them, they will immediately, unconsciously pick up on it, and return that excitement. Conversely, if you don't trust someone, or think they don't want to talk to you, they wont want to talk to you, and they won't find you trustworthy, either. It's a counterinruitive, ready-fire-aim thing. You don't need to be perfect at this, you just need to be aware of it. People are excellent at vetting intentions.
Third: The idea that there's somewhere you can go that will make socialization easy is a farce. Interaction is "permitted" everywhere, and you can try it anywhere. Go for several short conversations instead of putting all your effort into one. You should be fishing for enthusiasm: if you get no effort back, then it is unwanted. Drop it and try again with someone else.
The whole point of bringing groups together is to encourage people to interact. It’s awkward for everyone, but you can make it less awkward for others by just being friendly.. complimenting someone, or even just asking a simple question to get some engagement.
As long as you are respectful, friendly, and not pushy, everyone will respect you back.
Try to find some local gatherings in your own community, maybe a church potluck (they won’t care if you’re not religious, they are just happy you are there) .. maybe a local game shop has some DND evenings, or just find something that aligns with your personal interests.
To improve your nervousness about speaking, toastmasters or a Dale Carnegie class are both good options as well.
Most places will start by giving you some training materials on how to initiate friendly, non-threatening interactions with the customers. These are basically to burn some non-business cycles with the customer to prove that you're not trying to hard-sell them by using aggressive and manipulative techniques on them[1].
There are a lot of open-ended, safe topics you'll use for this. But once you get comfortable with the technique, you'll realize that you could use almost any question. Even rather specific ones like, "What's your favorite sandwich" can start a perfectly fine conversation with someone. Most people like new, unpredictable utterances and as long as you present it as non-threatening it can lead to a fruitful conversation.
Along with this you'll learn to time your speech to provide plenty of spaces where your interlocutor can cut away if they so wish. E.g., if you've told 3 pithy little stories which were each less than 15 seconds, they will feel at ease staying for one more before they go away. If on the other hand they aren't able to predict whether your next story is going to be a fun 10 seconds or an excruciatingly dull 5 minute rabbit hole, things are going to get awkward real quick.
Finally, if you don't listen you won't sell shit so you will have a nice daily scorecard on your progress.
1: It's amazing how well this works. Hard-selling commissions must be so razor thin that the salespeople can't even spend 30 seconds to build normal rapport with another human being. I've literally never had the experience of an employee starting out as a human being and then pivoting to aggressive/manipulative tactics. But maybe all the salespeople who excel at that are employed by big pharma and since I'm not a doctor I don't have contact with them.
What kind of therapy do you look for for things like this? As someone deeply inverted, prone to "creatively interpreting" things in a negative light, who dwells on imagined sleights, etc. I've thought maybe I need some professional help. But I'm kind of afraid of talking to people about my issues in general so I don't know what kind of therapist would work for me.
The most important (and hardest) part is finding a therapist you trust.
Love yourself first. If you truly believe that you have value;
that when you open your mouth and speak to others, you brighten their day;
that when other people meet you, they are happier or smarter than they were before they met you;
then it is your natural obligation to talk to other people (don't dehumanize them by calling them strangers), because you are giving them the gift of your own special human light.
I realised that after the COVID lockdowns people were so starved for contact with other people that any interaction would make their day. You don't need a pandemic for that, you can always make peoples' day just a bit better by saying hello.
If they don't want to talk you should be able to recognize it instantly.