I'm guessing with a 1/3 of an acre paddock, dragging isn't going to be an option. (SUJ, with larger acreage, I absolutely agree with you - dragging/harrowing is a great way to manage manure. We use a homemade drag too.)
And while spreading fresh manure on a garden can work if you're careful, I suspect the OP's neighbor's wouldn't notice any difference in the sight and smell of fresh manure in the garden and fresh manure in a paddock.
To the OP - if there are commercial greenhouses or yard and garden centers near you; you might very well work a deal with them to haul your manure away. Hobby and backyard gardens tend to only want the composted manure in the spring, when they're first working the soil - they tend not to be a reliable, year round resource.