Cliff,
The netting you described is what I use in my bass boat. I put the big pinch on weights that catfishermen use with the ears on them around the edges for weight. I drape it over the trolling motor (my biggest line grabber on the boat). I put duct tape over the cleats. You can still tie a rope to the cleat but the tape closes the line grabbing ends of the cleat. All boat flyfishers should have a roll of duct tape in the boat to tape over line grabbers of various types.
Robert