"Women workers here use an honor system and take very seriously the need to only invoke this leave category when they truly need it for fear of ruining it for others.) "

How do you know they're not "abusing" it if there is no objective check?

"It is becoming a mess. I have had no issues with the women on my team, but a locally-employed man on my team (who has made it clear he is not a trans man) is clearly misusing this leave category. "

Do you only have 1 male working for you? If the others aren't misusing it, then your issue is with ine employee. Why would you want to change the policy rather than the employee?

"The letter of the law is not perfect "

Yet you don't want to get rid of it. Taking advantage of imperfect situations is only for women I take it.

"This law was the result of years of women’s rights advocacy"

So is everyone not allowed to benefit from the improvements created by another sex or is it just men?

I think a good solution would be to give all male employees an additional $100 each month to spend on bably formula since you know they can't lactate like your female employees. You wouldn't be able to ask them what they spent it on or whether they even have a baby. It's imperfect, but babies need to eat and it shouldn't be harder just because their parent can't lactate.

https://www.askamanager.org/2022/05/my-male-coworkers-are-insisting-on-taking-period-leave.html