I suppose my position is incredibly simple in that I just cannot see the problem with saying that a long term unemployed former miner simultaneously has white privilege whislt being deeply underprivileged overall due to his income, wealth, where he was born and lives, his health issues from breathing in coal dust etc etc.
I don't think it's actually possible to pick all of these things apart. I don't really think that you can abstract concepts like blackness or whiteness. They exist in terms of how they are experienced by actual individuals.
Members of what might be called the white underclass do not suffer disadvantage separate from their whiteness. Non-white elites, let's go whole hog and say some member of an aristocracy in Africa, are not advantaged seperatly from being black, being black is part of who they are and that is what makes them elites too.
All kinds of people can suffer from ethnic or racial aggression, across class. They can suffer classism and actually that can be against upper class people as well - there can be a very powerful class hatred in that direction.
I'd also just point out that there are black people who don't feel racism has been that significant in their lives, or that their race has advantaged them. John McWhorter has said a few times that black university students are often given advantages in that system, he feels that he was himself. If we wanted to take the language around privilege seriously, shouldn't it capture that?
All this is really to say, it's just a wholly incoherent framework. Models tend to simplify, of course, but make it too simple and all you have is garbage.