After almost a year from the opening this thread, here is the outcome:
Since my 5d3 was almost at the end of the warranty and had some minor spots on the sensor, I sent it in for a free cleaning before the warranty expires. Since I was sending the body in, I also sent the 50 STM and the 70-200 mentioned on this thread.
Took them 35 (!) days to service my gear, and when it got back here are the technician's reports:
- 5d3 was working fine, sensor cleaned
- 50mm STM was perfect, nothing done
- 70-200mm calibrated for both front and back focus
After I got it back, shot with the 70-200 for a week and WOW, it's much better now. Much more accurate and doesn't miss focus like before.
I'm happy that I finally got it working properly, it wasn't bad before but I was a bit disappointed for spending so much money and still missing shots. Was blaming myself, changing shooting techniques, trying all types of AF adjustments and nothing helped.
It sucks that such a high end product comes out of the box in need of adjustments that will leave you without your gear for over a month!