MFI pump thermostat cleaning

On the winter project list is cleaning the thermostat. The top screw on the housing took considerable effort to break. Without removing the linkage arm (not going there!) I won't be able to free the bottom screw. I really wanted to remove the complete assembly and do the hair dryer test, but as far as cleaning it, is it serviceable by removing the cap and drawing out the rod/disk assembly? I would clean the assembly and clean the bore of the housing while on the car. Is there a reason this won't work? Thanks in advance.

The short answer is:

Remove the cap, pull out the rod, clean the discs with carb spray (there's no real reason to disassemble the stack, but if you do, DO NOT MIX THEM UP!!), clean the bore, grease the rod and reinstall.

There's no reason to remove the housing or any linkage rods.