Yikes, that sounds like misery! Is there any way to put drainage piping (the kind with the holes along the surface) in to divert the runoff from streaming into your place? We used to do that back in IL where the soil was very much clay and houses were often built at the bottom of a small hill. I know, though, that it can be hard or impossible to find a diverting path that doesn't just end up pooling back where it would have run anyway. Hmmm, maybe a nice draining system that delivers the excess to that one neighbor's land ...
