I think the spindle mount is actually the motor housing. I would start with removing all the screws and that C-ring on the fan. Maybe there are more screws under the fan, but I am pretty sure that the spindle holder is part of the motor housing and can't be removed.
Anyway, even though you say you are sure that the noise comes from inside the motor, I'd start with removing and testing the fan. It is an externally powered fan (I think) so it is easy to test just the fan.
Edit:
I think I was wrong. The plate seems to be removable. How does it look like when you turn it around? On one of the pictures it looks as there are screws inside the air channels.