One way to disempower the false narratives and cherry picked analysis would be for schools that are out of equality "whack" (60%/40% ratios) are considered imbalanced in academic circles. I remember reading a statement that they need to keep it below 55/45%, otherwise the social ramifications become toxic.
Implement male gender studies or a subset of it in college, and institute programs which in a positive and structured way ensure all men of all colors have the appropriate access and make sure it is balanced.
Once this is done, it deflates a core premise of the MRA view that the "having one's cake and eating it too" goes away.
Lookup on TED talks where a leading feminist called out the horror statistics of male dropout in high school and then couple it with the higher education, and we have to realize we have a serious issue for boys. One can't mask that over because later in life as boys mature (hopefully), when women desire to hit other milestones (as men should too) the pool of what is deemed acceptable men drops like a rock following the socially observed 80/20 rule. 80% of a gender goes after 20%, and ignore the rest. This leads to a nasty scenario.
As you called out data wise (not doubting your analysis [my good/core intent], this has happend for 50 plus years, and look at the end results. (you are writing books on it).
One of the issues I have had with some journalists views is the swapping of percentages and total numbers when it suites a narrative. They should cover both, because in reality the percentage and ratio matters more, because just because there are more men also means there is more women in return. It shows a false view. Show both and talk to both or defer to the ratio IMO ...
As a reference, I am a male feminist and believe in equality.