The impossible to solve overheating problem

I would consider the water pump a cheap test. Replace it. They corrode and clearance inside the housing increases between impeller and the casting.
Bypass fitting correct size?
How is the flow at heater core?
Heater fan on high, heat on hot. engine at operating temp, both heater hoses should be almost the same temperature.

I had a heater core problem and clamped hose down.it created an overheating condition. Food for thought.

What is the bypass fitting? I actually have no idea how the heater core flow is. Could be clogged for all I know, you mean that the heater core should take some of the heat from the engine?