Your analysis of how it is very hard to separate race and power is insightful, and many experts on racism have argued that race and class are very similar pieces of a single power structure.
But I still think it's useful to compare and contrast the two "-isms" -- and to see how conceptions of both have changed over time. I really like Ta-Nehesi Coates's analysis of how over the past century or so, Germans, Italians, the Irish, and Swedes all became merely "White" in the United States.
You are also spot on that long ago in America the ruling class realized they needed to divide and conquer various disenfranchsied groups -- and so they began to convince poor Whites that they were in a completely different category than Blacks.
This gave even the poorest Whites a group to look down on. Writers as diverse as Freud and Thomas Ashby Wills have written about how people who are doing poorly like to find (or manufacture) a group to look down on.
If I'm suffering but you're doing even worse, I feel better by comparison -- though only in the short run.
Freud's scapegoating and Wills's making downard comparisons are very close cousins.
Thanks for this food for thought.