Do you have any sources for this "breaking it down on age, education, grades, jobs, actual experience (part-time vs full-time, overtime, time on leave) you find that most these differences disappear"?
I'm afraid most my primary sources are in Norwegian since I live in Norway, but I can start here. On average, women have an income of 326400 NOK and men 487800 NOK so about 67%, unfair right? Well, first of all 5.6% less of working age are in the workforce (77.1% vs 82.7%), I can't be bothered to cross-reference with medical or unemployment data but it's mostly stay-at-home moms, not that they're unable to work or unable to find work. In addition 34.7% of women work part time compared to 13.9% of men and without having the exact data here also overtime is male dominated.
Together when you plug those into the facts and compare full-time equivalents to full-time equivalents you find females make 87% of what men do. Breaking it down further this study (PDF) show that women prefer lower income, more risk adverse educations. This is also reflected in that the private sector is 36% women and the public sector 70% women, which generally is safer and pays less. In the study they find:
While the men in the application data have mean lifetime earnings of 12.46M NOK, weighting with the first choice probabilities, women have a corresponding mean lifetime earnings of 11.20M NOK, or about 10 percent less.
So now you're down to about a 3% unexplained difference. Now I'm entering a very touchy subject which I can't properly back up with data but my guess it's primarily maternity leave, as in Norway you have a total of 52 weeks, usually split into 42 weeks maternal leave and 10 weeks paternal leave and on average 1,78 births per woman. It makes some employers reluctant to hire women around 30 as they can't ask about such things and despite formally holding a job it's going to have consequences for experience and promotion opportunities. I know it would for me if I took that much leave.