Thank you. You just saved me a lot of frustration and at least 70€.
When I bought my 156 (2002 facelift), both side mirrors were tie-wrapped to prevent them from flapping. Unfortunately this also prevented them from folding normally so they ended up completely busted.
I had to buy new ones (150€ for both in used condition) and paint them (the pre-facelift ones where plain black just like the mirror mount)
But last night I found my driver's side mirror busted again (I had left it closed, so this was probably done on purpose). Fortunately this time it was just like the issue you described; no busted plastics.
I took apart the mirror following your instructions. The only difference in my case was that there was one more screw connecting the mirror's arm to the cap, under the rotating mechanism. I unclipped the mirror glass and removed the mechanism's three Phillips screws, then the last screw and it was off.
I don't have a vice, so I 'm going to use a friend's tomorrow, but I am sure everything will work like a charm.