I think you need to not only be happynow but happy later.
Remember anything that's planted now will grow UP and get fuller, do you think they will keep those hedges at 4' in the future.
You really need to stop it before it begins the work, it sounds like your neighbors are a bit of a jerk not to talk it out with U, fine that's there prerogative.
It's your prerogative to file an inquiry into the review folks or whom ever to tell them what's going on. Ask them what the limitations are and get a clear understanding about getting this work must require an approval.
I see you posted at the same time, good you are on the right track.
I don't like the word "suggested" that can't be enforced?
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