Unattainable 1:1 magnification with the JJC FDA S-1 and Micro Nikkor 60 2,8

The JJC FDA S-1 does not allow a 1:1 magnification with the Micro Nikkor 60 2,8. It only reaches a smaller factor (about 80%.
The probable reason is the excessive lenght of the original step-down ring.
Using a thinner step-down ring, as it has been done in this video, does not improve the outcome.