"And, how about those occupations that swing from "female-dominance" to "male-dominance" and vice-versa? Do they maintain their relative level of compensation, or does it change?"

Historically, it has gone down when women entered that industry (as we both know), but all the studies done in this vein have a key confound: they don't tease out ordinary labour force engagement factors.  Did the wages drop because women started working in the industry, and this was discriminatory wage suppression because it became "women's work", or did it drop because the industries were summarily flooded with labour?

Women didn't enter the workforce evenly, across all industries, but fed into specific industries - heavily -  which led to drastically different influx rates by industry. It's highly probable that female preferred industries were swamped with labour, which drove down wages.