Very few things carbon up like the muzzle brake of an AK-74 fired with Soviet 7N6 ammo.
I tried everything.... soaking in Hoppe's #9, soaking in Slip 2000 Carbon Killer, ultrasonic cleaner, etc.
Just by accident I found the one thing that really worked and that was Shooter's Choice Copper Cleaner.
It stripped the carbon off in an hour or so.
I'm not sure how it would affect aluminum or whatever the part is coated with but you might try the Shooter's Choice.
Brownell's and Midway seem to be out of stock, but you can find it from other online sources, including direct from Shooter's Choice. Make sure to get the Copper Cleaner.
Be careful to test whatever you use. I use a piece of scrap aluminum as a test.
Note that strong soap cleaners like standard Simply Green, Greased Lightning etc will DESTROY aluminum and anodized aluminum finishes and do so fast.