Run a test with a liquid metal thermal interface materials to determine the efficincy of your cooling stack-up
Using a test with a liquid metal thermal interface material, you can be 99% confident that resistance in your thermal system is or is not due to the thermal interface material. There are multiple liquid metal thermal interface materials to choose from, but one way they can be used is to dispense the material onto the heat spreader, compress it as a thermal interface material, and re-run your test.
Since the interface is metal, it will have a high thermal conductivity and in molten state, the contact resistance will be approaching zero. This is the situation of an ideal interface. If your system is still reading a high resistance, it can be assumed that the heat build-up is not in the interface, but in some other location of the stack-up.