Hi Everyone !!! :D
I wanted to share my experience and tell you about my next steps to solve the problem :
1/ I removed the 300K linear pots (and tone pots) from my LP classic 60 for CTS 500K audio taper pots.
2/ I changed caps for Hovland Musicaps
3/ The most important change of all : try a Suhr Badger 30 instead of the Bogner Shiva.
The Suhr Badger 30 is the amp that I've been waiting for a long long time... Now and for the first time, I can hear my Les Paul and the Mules shine through the amp, it is impossible to describe : 2 EL34 cranked with the set of Mules : I just can hear every fibre of the wood vibrate.
It's really an amazing musical plexi orgasmic experience !!! :D :D :D :D :D
Thank you so much Tim for your incredible products 8)
By the Way and to conclude, the Mule neck is absolutely not dark in my Les Paul anymore and never was, the problem was just the Shiva which is too dark by itself... I got now a WONDERFUL sound with the neck, I'm really very very very happy !!! :D