From the looks of it there's nothing imposed until you either 'admit' (as per the link's language) or 'deny' and have a hearing. This is not much different than many other forms of similar ordinances. And any time there's a 'hearing' that doesn't go the defendant's way there's always appeals. Sure, there's typically costs to file for such an appeal, but do it, every time. Their costs to provide for the appeals may eventually 'encourage' them to stop bugging you. The 'system' doesn't want to work any more than anyone else.
Is the rest of the animal control code online anywhere? Because section 7 mentions 'found in violation' and it'd be interesting to read what that constitutes (sections WCC 55.010-800).
I'd start looking into the ordinances requiring maintenance of property regarding the adjacent unmaintained acreage. I'm sure it varies by zoning, so know what applies for it. This as a means to ratchet up activity on the part of the county. Make them start working more and they'll start finding ways to avoid it. This is the 'squeaky wheel' scenario. Basically, with most laws there's really no way to avoid getting 'something' wrong. If the system isn't going to stop being a problem for you, then start becoming a 'problem' for the system (work-wise, that is).