4. A conversation I remember being present for (not firsthand as in it being my own responsibility, but a real situation):
Representative of an all-white community group asks "Why don't Black people ever want to join our group? We invite them but they don't come."
Advice in return: "They're busy already with all kinds of things. Instead of trying to get them to join in with yours, go and find theirs and contribute to what they're up to."
In their case, there _were_ Black-led groups in geographical proximity.
How that translates to your situation - well I don't know, but I'd be looking around at "adjacent" (in some sense) organisations for which are most "the opposite of yours" demographically, and finding out what they need. If you and other board members can contribute (networks, skills, money etc) to their mission, there's a chance for relationships to build organically and see what comes of it. And it gives you a chance to learn from how they do things - even simple factors, like what time of day are their meetings.
@neil