I wonder if any of the governing bodies would want to be the first to require it. The comment Mike Craig mentioned about the NSA being worried about a lawsuit, for instance. They probably don?t want to require it and then be sued when someone still incurs some sort of injury despite wearing the mask (nothing one of their lawyers couldn't fix with some CYA language). Those organizations may also be worried about their revenue.
Seems like you have to target those orgs plus maybe the NCAA? Maybe with a general campaign that highlights player injury stories. Like someone else said, it would help if you had someone with personal experience, or a group of someones. Maybe you could find some physician(s) who's vocal about it?
WearTheMask.org is available for $15
You can create an online petition and embed in your site or blog:
https://www.change.org/petition
If you build awareness via Fastpitch forums like this one, you could invite people to like your site/facebook/twitter/etc to contribute stories and photos.
Re: the NCAA?
This article talked about the NCAA not being ready to enforce masks because "because the equipment is in the early stages of development, and there's not enough research available to ensure that a product exists that would truly protect players."
http://www.recordonline.com/article/20150531/SPORTS/150539934
It also talked about NOCSAE (National Operating Committee on Standards for Athletic Equipment)
"NOCSAE sets the standards the NCAA uses for batting and football helmets, but the organization does not yet have a standard for softball facemasks for defensive players."