I finally got it! The key for me has been to study a bit until I understand what could allow to minimize the length of the back and forth of each block. One way to order worked and I was happy to won. Had no big fun looping in all direction so I'm glad it's behind me.
This level is simultaneously very interesting as a concept and kinda null as a solving experience, since (at least to me) it really felt just like guessing a combination lock until it worked.
Well, I had serious troubles, here. Still not sure, WHY this variation was the fastest. I see, many people got that fast. Not my story, here, though. I think I brute forced it. Huh. :)