Actually, if the organizer had paid any damned attention to what you said earlier, this wouldn't be happening!
I wouldn't count on her being at all sympathetic or helpful.
I think I'd say to the organizer, "I'm going to organize the get-together, if you don't mind. Then I can make sure it will work out for me."
Then when you decide what to do, you invite each person *individually* and *directly* (no group of mass emails!! In fact, don't email at all). And when you invite them, you say to each person, "I'm putting together a small group to help me celebrate my birthday. I'd like you to join me. The group is smaller than normal, so please don't mention much about it around the neighborhood, etc., because I don't want to make people feel bad if I didn't include them. And please don't invite someone on your own, because I'm keeping it small."
If this particular friend, the Organizer, brings up Bully Neighbor, just act really surprised, and say, "I thought I'd told you, I was simply going to drift away from her. She doesn't seem to actually like me that much, so why would I want to spend my birthday celebration with her? Please respect my wishes."