Thanks for all the great ideas. My focus is on the exception to the paragraph that explicitly allows household pets.
Livestock and Poultry: No animals livestock or poultry shall be raised, bred or kept on any lot,EXCEPT, THAT, household pets, in limited numbers may be kept provided they are not maintained for any commercial purpose.
By definition a pet is simply a domesticated animal and "domesticated" is defined as any animal that depends on human beings and cannot survive in the wild.
Interpretation is 9/10ths of the law, and it's your lawyers job to convince the judge to interpret it your way. I've been involved in court cases that were a lot harder to win than what you have, I think you'll be OK. However that will depend on the judge.
We have other experience with HOA's, not necessarily with chickens, but: does anyone else have chickens in your HOA subdivision? If so, you may have an even better case.
We erected a structure that was technically "HOA pre-approved" but received a hate letter when they objected to the siding that was used. I canvassed the entire neighborhood, talked to the people that had the same type structure (at least 20 others), approached the HOA with pictures and they proceeded to send the "violation" to their lawyers. I retained a lawyer who basically just laughed when I told him the deal. Sent him the info and a (small) check, and the HOA dropped the issue like a solid lead balloon.
Point being, at least in AZ, restrictive groups (HOAs) are not allowed to selectively enforce and by allowing other houses to do so set a precedent of allowing those rules to be bent. It's like discrimination, but on an HOA/housing/law level. It doesn't expunge you of wrongdoing, but it muddies the waters enough legally to typically have your case thrown out for the time being.
However, if your judge is pro HOA and hates chickens, ouch.
Good luck!
Hopefully some of this makes sense. Feel free to ask questions, I'll elaborate after some sleep.