Okay, so I bit the bullet and started a Facebook page for my game.
https://www.facebook.com/HeroesAndTreasure/
Not quite as bad as I was expecting, though the whole social media marketing thing is just not in my wheelhouse. Having to constantly post updates, for example.
HOWEVER..
Facebook makes stuff pretty easy. I was pleasantly surprised that it was easy and obvious how to schedule posts for the future, so I can write up a couple of posts in the evening and have them appear at different times the next day. Makes this much more doable.