It would happen if we could persuade more men to just make that tiny effort
Man the message is way, way out there, already. There are loads of different feminist saying things in loads of different ways. Some loud, some quiet, some sweet, some vicious. The problem is some/many/most men just don't care enough. You can't make them care by speaking in a different way.
The messages out there are getting to the ones who do care (loads of young women and girls as social media shows...and the dervels of the men). Modifying language won't suddenly make the rest of them care...if anything it'll make feminism look weak and insignificant.
Not I actually thinK the NAM issue is that big a deal. NAM isn't used by people who would otherwise be allies. If no feminist ever again said anything without a qualifier then derailment, attack and disagreement would still exist to the same level IMO.