Hi I have been reading your post and I don't know if it will help but there is and Act (The Allotments Act 1950), it overrides covenants etc and has recently helped many, many people to keep poultry when they had previously been told they couldn't (even by councils!). Cockerels are then subject to a Noise complaint and the council should then make the necessary arrangements to take noise level recordings, I take it this hasn't been done. A compromise than then be met by using a darkened Cockerel Box etc.
People like your neighbour really get on my nerves, our in-laws have a farm and their neighbour regularly complain, my responseis if you don't like it GO AWAY!
Just for your information there is an excerpt from the Act below:-
The Allotments Act 1950, Chapter 31, Section 12 states that regardless of clauses in leases/ tenancies/ covenants/ contracts or agreements to the contrary, the occupier of any land can keep hens and rabbits on it, for their own use, so long as they set up and maintain adequate housing and so long as they make sure that the hens/rabbits don't become a nuisance or pose a threat to health.
(Navigate to the Office of Public Sector Information website (opsi.gov.uk) and search for Allotments Act 1950 to read the full text)
P.s - Are your Orpingtons Large Fowl or Bantams?. If they are Bantams I may be able to help.