“Non-queer queerness” is using queer in first an external, then an internal sense. The feeling you describe makes sense to me, I think that gender identity or coherent body image or whatever you want to call it exists on a spectrum like sexuality (which is obviously not to say uniformly distributed). You’re internally ambivalent to some degree about your body or gendered self - I think many people experience this to some degree. So I think it makes sense to say you have an “internally queer” experience, as distinct from an non-normative social identity or way of living, i.e. the usual external meaning of queer.

Do you find that this makes it more difficult for you to define meaningful goals for yourself? I think many men don’t just want to be a good person, they want to be a good man, meaning good husband, father, provider, protector, etc. If you’re ambivalent about your gender I could see that link being weaker.