I’m no lawyer, but...
The 10 sq ft per bird appears to apply only to chickens. The limitations on population appears to apply to your breeding stock only since their offspring (or introduced offspring—but I wouldn’t mention my auction habit if it were me!) will be sold or harvested at or around 8 wks of age.
I interpret the waste disposal bit to apply to all appropriate storage/disposal methods that don’t result in objectionable odors. That would definitely apply to well-maintained compost bins and/or deep litter. In fact I’m not sure anything else would even suffice. Just throw a nice-looking canvas tarp over the top of the bin(s) if anyone comes to call. You need tarps for rain anyway. Make sure there’s not a lot of nasty wasted food lying about—rodents and all... I’m not saying you’re not already doing that... pretty sure you are.
I’m really surprised they don’t explicitly exclude roosters. The only potential problem I’m seeing here is if they interpret the run to be a structure, and it buts up against your fence—or if you have other “structures” within the 10’ setback. You could argue that as they have no foundations, they’re just semi-mobile pieces of furniture that might be anywhere in the yard & that your wooden fence (you have one if I’m remembering correctly?) serves the same purpose (of not violating your neighbor’s unimpeded use of their property) as the 10 ft setbacks are intended to serve.
Be kind & diplomatic if you end up having to talk with anyone, but I’d avoid being too deferential. Otherwise it seems that bureaucratic types tend to serve the most insistent at the expense of the common good.
This doesn’t look as bad as I expected. I’m thinking it’s not actually going to be a big problem for you. Hope not!