Update
Before I went to CM, I went to CR IO and they again confirmed that they could not extent my visa. They were quite insistent.
In CM IO with my 3 nights hotel TM30, I was asked (as I expected) about my residence. I told truthfully that I lived in CR and the IO asked (as expected) why I didn’t extent in CR. I told him the CR IO said they couldn’t and his reaction was a confirming "yes".
So I got my extension and the note that I had done my first 3-month address notification.
Coming back to CR, I have made sure my landlord has registered my anew (TM30). That must be enough to keep me in the clear.
Thanks again for your help.