It's frustrating that the only suggestion the experts interviewed have here is essentially blue-washing woman-dominated jobs. "For instance, many health care jobs could be framed as roles requiring the strength to lift people. Preschools could highlight the need for teachers who serve as positive male role models." Just reads as that one SMBC comic - "how can we make math pink ?" As if the only way they can understan…
Isn't it only a question of marketing? There's only so many lumberjacks needed in an economy. Sure you can depress the wages for awhile but there's still a limit. So you need Men do to something else and the way you do that is with marketing (and also with Men being unemployed until they accept a nursing job).
There have been some studies that show once female participation in a field/career gets past about 40%, males tend to leave (or at a minimum, fail to enter) that field/career. Historically, school teachers and secretaries were male fields. Then in WW1, there weren't enough men available, so women were encouraged to enter those jobs. After WW1, those same jobs weren't seen as "manly" enough and male participation never recovered.