Little update of my situation...
I was to impatient to know if the tube was the issue, I ordered last week a cheap 6080 from Tubedepot.
The 6080 received 2 days later, I installed it and since... my Crack works perfectly.
So there it was... the 6080 tube...
THANKS Paul and everyone for the help to troubleshoot my Crack. The good point is that I practiced a lot (I mean a lot !) my soldering skills. I think that it helped me during the speedball upgrade I've just done tonight. So nothing happens for nothing... I've been listening for music for something like an hour tonight with the speedball upgrade and I enjoy every seconds of it.
Next step, try few others 12AU7-like tubes. But no rush, I just need to enjoy the music now...
Have a good night (/day)