Town officials said nothing that's a roof of any sort (many suggestions have already been made, everything has been shot down and only wire is allowed, so the structure legally counts as a pen). OP recycled her old roof panels as winter windblock for the run, and put up giant patio umbrellas because umbrellas are free standing and thus can't be considered a roof or building structure in any sense of the word.
On the plus side town officials did agree the chickens and their set up were fine where they were so neighbor was out of gas in trying to find ways to get rid of them, and now has a lovely view of umbrellas from his bedroom. I suggested painting HAVE A NICE DAY on top of umbrellas.