Hm, yeah, I would just start up a Mastodon page in parallel with the Meta page. Pick the right “home” server to join; that’s critically important for Mastodon in a way that it’s not for Meta. Put in charge of the page someone who’s genuinely excited about participating in Mastodon, and would be engaged with the gaming community there whether or not they were in charge of the page. I don’t think I would recommend spending anything on ad promotion of the Mastodon page, but like I say I’m not convinced of the utility of spending money on Meta promotion either. YMMV
Anyway like I say my level of knowledge about it is pretty minimal but I’m happy to talk more in depth on details of my experience also if you like.