I did some fiddling outside this afternoon and made some improvements already, before I realized my ridge line problem. I was using the triangle thingies that come with the UQ, and connecting them up to the end points of my hammock with mini biners, but I have found it works much better with a Byer Moskito when I connect the shock cord sides directly to the outermost strings on each corner of the hammock. That greatly increases the UQ's tendency to spread out under the hammock. Also I had the ends cinched down way to much, if you overdo it it wants to pull the sides of the UQ together. The path of least resistance is to go underneath the hammock rather than up the sides. So I loosened the ends and tightened the sides and it's way better already.
Also, as SilvrSurfr has discovered, the Moskito just doesn't work as well when it's upside down, I don't know why. I flipped it back up and things were much easier with the mosquito netting above me.