I don't have much info to offer (except moral support!!) but you might try researching cities that have recently amended the ordinances to allow chickens (Asheville, NC for example), if only to pull verbiage to support your arguments.
There are loads of folks on here that have been in your exact position and can offer accounts of what worked for them. These same folks are also very helpful proofreading and providing additional points of argument that can help swing the HOA folks in your favor.
GOOD LUCK!!!