Well it sounds like the previous owner adjusted idle speed to keep in running on 2 cylinders.----So now you have to find the idle stop screw and adjust for proper idle RPM.
Your location ?----Have you checked gear oil ?----And 120 PSI seems low for that motor.----Do you have spark?----Carburetors clean ?----Choke flappers closing when you operate switch for choke.-----More details on this " shedded " propshaft.
What is the shaft length of your motor?----Or transom height of your boat ?---Is the 36" the length of the shift rod itself ?----Or post the actual model # of your motor to get an accurate measurement for shift rod installed height.
You tried to hone cylinders without taking motor apart ?--You re-used a head gasket ?-----First I have heard of anyone trying that.-----The motor needs to come apart for a proper rebuild.
I do not believe these motors left the factory with an overheat warning or shutdown system.----It would run till it destroyed itself.------A wise man would install a new factory impeller every 3 seasons !!--A " new to you motor " must have a new impeller installed.
It is a 2 stroke engine.----You mix gas and oil at 50:1 in your fuel tank.----I suggest you read a manual for that fishing motor / talk to some fishing buddies before launching your boat.----Could save you a lot of beer tokens.
That looks to be a 1969 model motor.--Picture of cowling will verify that.-----The 68 models had finer / smaller teeth on the flywheel.------And in the french speaking part of the land.---Take a good look at wires on the motor as they are often corroded , with insulation...
The primer bulb is nothing but a manual pump.----It moves fuel.----And most able bodied folks can generate much more pressure by hand then the PRESSURE fuel pump on your motor.----Elegantly simple testing can be done.
