An unintended proposal:
I would be the first to admit that generational wealth difference is not the only disadvantage that POC face. Still as you point out there is a large inverse correlation between POC and generational wealth.
This suggests an approach that might find far more commonality across political lines:
Explicitly tie affirmative action to the historic wealth of the parents. Sure there will be many counter examples where this over or under judges the need of a given individual.... just as a race based rule will do. But politically it might be supported in a far broader way. Such benefits would apply to all ethnic groups based on their start in life, and would disproportionally support minorities that need it most.
This relates to a second idea affirmative access instead of affirmative action... will write that thought separately when I get a chance.
At core I very much am agreeing with your points that that POC are disproportionally affected, and that the present system basically affirms the wealth's offspring in a way that needs to be countered. Cheers!