Not only have I ended phone calls with my initials, I have used them at the drive thru.
That's a sure sign that you're working too hard.
Social interactions are incredibly complex, just like air traffic communications an procedures. We have managed to create rules for everyone to follow.
I think the difference is that, generally, ATC communications while complex, are totally objective. They're formatted to rule out any misunderstanding through misinterpretation, and feelings and personalities have no function in them. A vector is a vector, a clearance is a clearance. The controller's function is to separate the machinery, and the pilot is simply part of that mechanism. (That probably has a lot to do with why certain controllers are so popular with this site's listeners. They let their human side show, which, good or bad, makes them stand out from the rest.)
Social communications, on the other hand, are so much more subjective. Body language, tone of voice, how well two individuals know each other, all play a part, but even moreso, whatever the topic of the conversation is is much less likely to fit neatly into a standard format.
The rules and format allow for a wide variety of information to go back and forth, but the structure is always (usually) the same. That is one of the difficulties teaching people on the spectrum how to function socially. It is the unusual situations that I'm looking for help with.
Even the 7110.65 10-1-1 d. has a problem in dealing with unusual situations, "Because of the infinite variety of possible emergency situations, specific procedures cannot be prescribed. " While the "emergency" part may not apply, I think the "infinite variety of possible... situations", certainly applies to social communications.
I'm not sure there's an easy answer for you in trying to emulate ATC communications...