Wow, what has your neighbors so worked up? Is the easement right up against their houses or something?
I’m sure you’ve already thought about this, but have you tried to talk to them nicely about what you could do to make them feel better about the easement issue?
If they aren’t willing to talk, I think you might have to talk to a lawyer, unfortunately. I’d hate to see you spending thousands of dollars trying to fix this mess. Good luck!