So I changed my layout into something HIWATTish. From the front side to the back I have: pots - turrets - preamp tubes - power tubes.
I think I have a bit more hum.

The cracklings and parasiting noises came from a faulty presence pot. I took it apart to have a look and I don't see why it doesn't behave normally. I ended up changing it.
I still have the same problem; massive hum; with the clean channel.
When I first fired up the amp; and it will turn out I had forgotten to wire the presence pot; the clean channel worked fine despite a low volume.
Wired the presence pot and the hum came back. I moved a bunch of grounded wires but with no luck. The mid pot from the dirty channel actually interacted with the volume of the clean channel.

Right now I have my clean like this : 1/2 tube -> tonestack -> 1/2 tube -> volume. The hum is slightly higher than on the dirty channel. I will try to put a resistor between the tonestack and the 2nd half of the tube.
The dirty channel is fine. I got rid of the 'bright' switch. I still have the boost switch but it gets really noisy when active so I will take it off.
I have 2 toggles switches wired to pin8 of V2:
_ n°1_ I have a 4k7 resistor that's parallel to the 4k7 resistor on the turrets, so I can have 4k7 and 2k35
_ n°2 _ Also in parallel I can add a 2.2uf or a 0.68uf cap
It's interesting to realise what they do... and how much noise they can bring in. I'm going try 10k like the JCM800.
About the layout, I could go back to the classic Marshall type but having this laydown output transformer doesn't facilitate things.
The pic shows my initial build. I had the heater wires running along the OT's. What would be a better option:
_ moving the heater on the other side of the tubes, between the tubes and the board.
_ using a buss wire
_ standing-up heater like Fenders