How would one do this without them being able to tell who made the call?
It's easy. The address.
The point is to report YOUR address several times, so they get used to coming to [Your Address] and each time, it's a false alarm. You can tell them it's a neighbor.
They'll get sick of coming out to [Your Address] kind of like the Boy Who Cried Wolf.
Then you have your gathering -- when the wolf actually shows up and kills the sheep -- and no cops will come that time, even if a neighbor DOES call the cops on an actual gathering. The cops will say "sure, sure... I come out to [Your Address] for yet another false alarm? I don't think so! Good bye!"