Scheduling playdates for your son is a recipe for bitterness and disappointment. Without feedback or direction for what the proper behaviour is, the end result will be ridicule and ostracism. Over and over. And this will continue into his adult life.
Since your son has no "feel" for interaction, the best you can get is an "intellectual appreciation" for correct behaviour. He has to learn the skill that everyone else will pick up naturally.
The first half is to get him to want to learn. You do this by rewards and other incentives, as outlined by any of a number of teaching methods. Sit down with him at regular scheduled intervals, be sure to show appreciation when he does things correctly, and show disappointment when he screws up. When he screws up, do the disappointment thing *quickly* and move on. Promise him a big reward at the end of a semester of these if he does well, and follow up on it (take him to an arcade, get him a specific toy, take him snorkeling in Hanauma bay, whatever.) Little rewards at intervals is good too (take him out for ice cream, his special time with his dad &c).
Make him want to change.
The second half is being able to recognize his behaviour *yourself* and communicate to him instantly. I cannot describe how incredibly difficult this is, you have to be alert for specific patterns and people are just not wired to do this. People go through their daily lives on autopilot, and don't normally evaluate what they're hearing/seeing/doing on a continual basis. It's s a difficult skill that needs to be developed through discovery and practice.
The problem with therapists is that the feedback isn't immediate. The therapist might be able to analyze and correct and connect with your son, but your son will tend to forget outside the session. Like I said, most people are on autopilot and changing the autopilot programming is hard.
When you get the ability to recognize his behaviour, simply say "ding!" when you see it.
It's immediate feedback, and when he hears it he should stop to consider what he's doing and change his behaviour. That's all it takes.
Be very clear that saying "ding!" doesn't mean you're angry with him or that he should stop or that he's being punished. It's simply a signal, and it's not meant to get him to stop, it's meant to get him to *think*. Also be very clear that he can ask you why you said it, and that there's no penalty for doing this.
Start with small, obvious behaviours such as repetitive habits or sentence construction, then slowly work into tactical advice (always look someone in the eye, always ask how they are doing, always remember their name), then into strategic advice ("never lie to a friend", "never tell something told to you in confidence"), then into planning advice (see what other people do and imitate them, dress like them, try to act like them).
Get a copy of "How to Make Friends and Influence People" (Dale Carnegie) and use it as a syllabus for what to teach. Also check out "Influence, the science of persuasion" as a guide for what to watch out for (so that others don't take advantage of him).
Best of luck to you.