Heater Door Actuator Clip/Arm

Do the hoses to the core both get hot and to the same temperature as the radiator hoses? What temperature does the engine get up to?
One thing to do when you do the flush is to flush the core on it's own with a flush gun, then do the engine. The flush gun uses air to create turbulence in the water and helps break loose any crud. CLR will work okay, as will most of the acid flushes sold.

Now I cannot say that blocking the bypass hose to push more coolant through the core is a good idea, but you can get a valve to install in that line that would restrict the flow as a test.

The Teflon should not be needed. I would try a different cap or two and see if it is the cap or the tank.