Use a piece of bungee around your thigh and put the map underneath.
I like to have the map drifting around in the bilge water.
I resolved the issue in the later paddles by sticking the map to the boat with leftover freeze-dry kumara and mashed potato. Seemed a good option.
I just stick it to the floor in front of me with the compass looped around the map case holder so I can tell which way north is. Problem with my compass this time though was if it wasn't lying flat, it didn't seem to work and yes it was a southern hemisphere one.