Ive only ever replaced a t/stat with the engine out, but I don't feel its a difficult job in. Im not sure you need to remove the alternator, but that's a job that gets easier after a few times.
I test the t/stat by hanging onto the top radiator hose from a cold start. When the t/stat opens from a fast idle, you can feel a flow of warm coolant through the hose if its working ok, it takes about 5-10 minutes. But its a definite change of temps and will get warmer.
Hoses should be firm, not rock hard. Rock hard is a often a sign of a head gasket leak.
Pressure in the system stops big steam bubbles forming around the cylinders. Once bubbles form in your cooling system basically throws its hands up and surrenders.
A bad rad cap is often the root cause.
The position of your sensor is right in the cylinder head.
I'm wondering if its giving you the temperature of the combustion chamber rather than the coolant. Temperatures in those areas get a lot hotter than the coolant.
Normally the sensor is on the coolant outlet where the top radiator hose connects to the head.
Did anyone alter your injector pump fuel settings when the turbo went on?