The ideal permaculture solution would be to build chicken tractors or an egg mobile and move those birds daily to fresh grass, allowing all that wonderful manure to fertilize the land. But that requires a completely new system.
Another solution would be to find a way to process that poop and turn it into a product that people will pay you for.
Have you seen this video?
Salatin composts all the blood and guts from his butchered chickens and rabbits, as well as any other manure and animal byproduct (feathers, dead cattle, etc.) that accumulates. No sell and minimal rodents or other vermin. The key is having access to the heavy carbon base (wood chips). All that nitrogen needs a lot of carbon to absorb it.
You would need:
1. Some pace to pile up and store the wood chips, having them on-hand for when you need them.
2. A regular source for wood chips. Is there a country tree-trimming crew that would be willing to dump the chips on your place?
3. Some means of mixing the chicken manure with the wood chips. A front-end loader would be sufficient, I would imagine. You've probably already got one.
4. Once you mix the chips and manure, you'll need a place to let them sit and compost. Salatan leaves them for 6 months or so, and then re-uses the same chips a second time. As you can see in the video, he's got a massive shed with open sides where the chips are piled up and the composting takes place.
5. A manure spreader to spread the composted chips and manure a year later.
With minimal investment, you might be able to turn a problem (complaining neighbors and stinky piles of chicken poop) into a money making solution (a garden byproduct that people will pay money for). Thus, the problem becomes the solution. Sell it by the yard as a garden amendment. I'd buy it if I lived anywhere near you.
Best of luck.