If the $ hit would be more than you can bear, try to "be the change you want to see in the world" bla bla bla.
Can you be the neighborhood social butterfly? Can you invite invite invite over for playdates, casual dinners (e.g., "We are putting a pot of spaghetti on, see you in 20 mins?"), birthday parties, holiday gatherings, pot lucks, and the like?
I'll tell you, I am an introvert. And busy-ish, but I do the things I mentioned above because even though I value my alone time, I also feel like if I don't know my neighbors I am seriously bummed out.
And I want my kids to feel connected.
And I don't mind a bit of mess in exchange for the wee bit of effort it takes to set an additional four settings.
And I don't give a sh!t about things being reciprocated. If I invite you, I invite you.
What do you think?