Sounds potentially ASC-ish to me. I?d chug along and get an assessment. If your DS is doing it persistently in lots of settings when you?re not around then it?s unlikely to be anything you?re doing wrong.
Some tools that helped my ASC-ish son to do what?s necessary are: regular routines; simple limited choices (this or that); visual timetables (even for kids who apparently very verbal!); and basic social stories (though for these you probably need some assessment first so you know where he?s starting from).
I had a real eye-opener when my son (now diagnosed with Asperger?s) saw the speech and language therapist as part of his assessment. First they had a lovely conversation about maps ? one of DS?s interests. Adult, sensible, good vocabulary, responsive, mature, to and fro, eye contact, the works. Then the therapist changed the subject. And DS just didn?t know what to say. Not at all. He went dead silent. Turns out he controlled conversations (and other interactions) because he had to, he didn?t have the adaptive skills to do anything else. And DS would appear confident with strangers because he very outgoing and wasn?t making the distinctions most kids make between known and unknown adults.
I wouldn?t go looking for a specific diagnosis myself. Keeping a log of problems and oddities is a good idea. Let the professionals sort out the label. The psychologist said DS might not quite tick all the boxes but gave him the diagnosis anyway, these things are not black-and-white. I?d even say the right help is more useful than the perfect label, and certainly DS?s diagnosis has got him the right help.
(by the way in my area help with social skills is available to kids in private as well as state schools, since it?s a joint NHS/LEA service. )
Best of luck!