So now that we have established the ducks are not going to get any quieter and you do not want to rehome them, it is time to sit down with your neighbor. Invite them over for a meal or at least a snack and discuss the situation with him/her. Find out what exactly is the problem and do not settle for "the ducks are noisy". Is there a specific time where its a huge problem? Does he/she have young children napping etc. Until you determine the exact, specific issue it will be difficult to determine a course of action. Share with the neighbor how important ducks are to you and how they are such a big part of your lives. Show them the duck run and all the effort that went into it. Make them see that they are integral to your happiness, otherwise you become "that" neighbor who has a flock of annoying ducks.
Invite the neighbor over and find out if there is something in particular that is driving him/her nuts and help her understand how much the ducks mean to you. Most of the time there is a root cause that is then covered up by "your animal is noisy".
She will need to do something, if the neighbor makes that "call", GUESS what, all the ducks will have to go.
I think rehoming a few versus, all of them with HUGE fines is probably worth it. Hopefully, they can rectify something with the neighbors because Neighbors that are NOT understanding will Make that call because they could careless about "your Happiness". If the call is made it's going to be a HEAFTY Fine PER animal and they will need to be gone in a short time.
Unless you can do what a friend of mine did, SHE put up a FIGHT and had the RULES change, she lived in a place where they could NOT have any chickens or ducks now they can have a limited number of them.. So if the "call" is made get ready to either FIGHT and have the RULES change or be prepared to get rid of them all.
Crossing fingers something can be worked out with the neighbors, but even if they do make the "call" I bet they deny it..