I am another cis man who suspects I would have been just as comfortable had I been born a cis woman, and I have independently come to a similar conclusion. I feel no need to emphasise my social or physical "masculinity", but neither do I make any effort towards being non-gender-conforming — I am perfectly happy having a beard, being hairy and wearing "men's" clothes. Conversely, if I had been born a woman with my same congenital personality, I think I wouldn't have made a particular effort to present my "femininity", but I would have been perfectly comfortable being less hairy, having boobs, and dressing and behaving as do some of my female friends (who are cis and hetero, homo, and bisexual) who, without being GNC, are not necessarily super-feminine.
What I would really like to know is whether I'm right in my intuition that certain cis-male and cis-female individuals feel the opposite. I imagine that cis men who enjoy "feeling like a man" or showing manliness (within the non-toxic and healthy range) are pretty sure they would have hated being born a woman. The same goes for cis women who love displaying their femininity; they probably feel they would hate having been born a man if they were to be asked.
(There's always going to be people that recognize me for what I am. But, for the most part, they don't insult me about it to my face, or even mention it at all.)
That said, I suspect that at least some "cis by default" people would indeed experience feelings of a brain-body mismatch if they had different parts, it just happens to be something you can't test for.