My husband and I figured out a pretty nifty way of dealing with those tarps. We inserted flexible PVC into flag pole holders we mounted to each side of each run, forming arches over which we can drape the tarps, and then secured the edges of the tarps with bungee cords looped through the grommet holes and wrapped around the top of each panel frame. It sort of forms a big umbrella-type look that lasts much longer than tarps simply stretched across flat, and it was really inexpensive to do.
My fix will be simple....just run a 2x4 or a 2x6 along one of the top beams, drape the tarp over it, and that slight slant and gravity will take care of itself.