Another possibility that someone suggested is to unclip the guttering and run a bead of neutral-cure silicone under the edge of the polycarbonate, just back from the edge, so the water drips off that into the gutter before it can run all the way back to the fascia. This sounds like a far more workable solution, but before I end up being the next owner's cowboy I wanted to check whether anyone could see any problems with this, or had any better ideas.