Take the total pay for both teams. Put it in a pot. Have the women play the men 5 times. Then divide the pot of money proportionate to the wins. If the women win 60% of the matches, they can divide up 60% of the pot.
My guess is the women’s team wouldn’t want that offer.
You obviously haven’t seen the Men’s team play recently.
I have to admit, I find your approach preferable. I would propose one small tweak, however.
Even one as hard-nosed as me would concede it might be too much to expect one side to play for free (or simply patriotic pride), so if one side gets skunked, and only if the final outcome was 5 games to nil (to toss in a little soccer lingo for atmosphere), the salary pot would be divvied up on the basis of the fraction of total goals scored by each side. At least that way the losing side - whichever one that might possibly be - would at least get something (well, maybe).