Uncouple the temperature sensor wires from the PCB and remove the northbridge heatsink.
You will find more dust under the heatsink, to be cleaned away.
Don't be tempted to take shortcuts with cleaning. The dust and gooey grime are functional threats to the health of your computer. And besides, you are a perfectionist, are you not? You would not own a Mac Pro 5,1 if that were not the case. See if you can make the board look as good as new.