Good luck with the HOA. Some are reasonable and some are not. I'd like to know the outcome of those talks before I made a final decision. How might that limit you in the future, especially if it means you can't have chickens if you get rid of those three. I don't think you have any more.
I don't have any easy answers. A lot depends on what you want. If you rehome any they will have to be integrated into the new flock. That might be really easy, whether it is one or three. People do one all of the time, usually successfully. But sometimes three is easier. From a pure integration into the new flock standpoint three is usually better than one but one is not usually a disaster. A lot depends on how much room your friend has and their integration techniques.
If you keep two, the pecking order could change, especially if the loud hen is the dominant one. Usually that is not too bad with hens, you might not even notice it happening. Occasionally it can get rough. You just never know.
If you keep two, will you add a third? If you do I'd suggest adding at least two more instead of one single. It can make integration easier.
If your friend gets all three will you get more chickens?