I know what RH thinks, and there has been a lot of speculation, but I don't think the Crankcase Breather hose is what causes the dirty TB plates.
And yes, remove the airbox.
Good luck mi amigo. Wish I could have been there.
What do you think did cause the dirty TB plates? That whole under-seat area looks pretty dirty/dusty to me. Does the owner live on a dirt road ? ? ?