"Yes, the bypass valve is also
"Yes, the bypass valve is also referred to as the poppet valve.
I would start from scratch, meaning drop the lower unit. At the exhaust housing, lay a straight edge across it and measure up to the bottom of the water tube. Make a note of it.
Now, measure from the surface of the lower unit upwards to that measurement you made a note of. That tells you exactly where the bottom ot the water tube will be in relation to the water tube grommet within the water pump housing. It should be inserted completely within the grommet.
If not, someone most like hit the water tube at some time when installing the lower unit and pushed/bent the tube upwards.
Dismantle the water pump and inspect it completely to make sure that all is as it should be..... water tube did not fold the grommet over, the seal between the pump housing and plate did not slip out of place, etc.
Melting that poppet valve...... the warning horn would have came on long before that could have taken place. When did the engine last run properly and what has happened since then that might have some bearing on this problem.
What are the cylinder compression readings?"