Welcome to force induction and direct injection. This was/is a known issue with my old MazdaSpeed6 with the 2.3 DI turbo. Intake valves would build up carbon due to the egr system. Without the valve washdown from the injectors, carbon can build up on the valves.
As stated earlier, walnut shell blasting was/is a highly effective solution to cleaning the valves(short of pulling the head off and cleaning/replacing).
Typically when you add boost to an engine, you need to add extra fuel to keep the combustion chamber cooler to prevent detonation or even melting of pistons. Direct injection reduces the need to add excessive fuel and you can lean it out slightly.
My superchaged mustang has a soot "issue" as well, but I don't worry about it.
Driving softly is another cause. Wind the engine out once in a while. That will help with the carbon build up in the engine and turbo to some degree. Not a perfect solution, but it does help.
On the video about the 2:30-2:45 mark, I'm not following his explanation. How would carbon build up on the intake valves cause a cylinder to run leaner? If there is carbon build up, that cylinder would be getting less air and run richer, not the other way around.