That's a good video for showing how much debris is there. I had mine pulled out when I rebuilt my 6.0L engine, but I did not have that on mine, so I guess it's a regional thing. Thanks for posting that.
In the video, he suggests using Simple Green. The common Simple Green corrodes aluminum, so I would not use that. I use Simple Green Aircraft cleaner, which is aluminum-safe, so that's an option. But the foaming coil cleaner is aluminum-safe and better for coil cleaning, so I'd recommend that.
From the video, it looks like you could clean the dirty side by only taking the blower out, not the shell. But if you remove the shell, I'd recommend cutting and taping it back up so the engine side of the shell can be removed easily, giving clearance for easier engine access for the valve cover bolts or injector work.
Aluminum Duct Tape for sealing.
Simple Green Aircraft Cleaner can be bought at Aircraft Spruce, Pilot's HQ, and Amazon. I only use it on aluminum, so it lasts a long time.