You should be able to hold your hand on the cylinder head for at least 3 seconds without screaming or it's too hot. That motor has a thermostat-----just something to think about. THe thermostat shouldn't have any effect on how much water is coming out of the exhaust relief. Be careful you don't run it hot. Check it with the old hand routine (be careful!!) regularly until you have driven in on the water and have confidence the cooling system is working properly. Go ahead and rebuild the carb with a kit and change your fuel lines if you haven't already. Be sure you don't lose the little nylon friction piece that keeps the choke lever all the way out so that the choke is fully closed or it will be a son of a gun to crank cold. Try to get the kit that includes a new plastic float if your carb doesn't already have a plastic float inside it. If it has the plastic float, you can probably get by with just a good cleaning. It has a fixed high speed jet and it must be spotlessly clean to run right wide open without running lean which can ruin it. If you don't have a special screwdriver to take out the high speed jet, then leave it in and clean it out with a good soaking in carb cleaner and some piano wire and compressed air. IF you try to remove it with a regular screwdriver, you WILL screw it up.

Good luck,
JBJ