The explicit advantages that white people used to have were considerably greater, so even though they arguably have unjustly many advantages now, they can literally "reclaim" the previous even greater level of unjust advantages.

If you steal someone's car, and use it as yours, and then you give it up or it is taken from you, and then you steal it again, it is still correct to say that you have "reclaimed" it. (Again unjustly, but "reclaim" only refers to the repetition, not the rightness of the matter.)

For instance, the 14th amendment could be repealed. The Civil Rights Act could be repealed, or Title VII could be rolled back to its 1964 language, and then whites would have even greater (relative) advantages, as they once did.

I think you're neglecting to consider this possibility because it seems so absurd and so horrific that it's not even worth thinking about. But if you think through the implications of what actual avowed white supremacists say, this is not just a formal possibility but actually advocated for by some people. We can reject it with great vehamence, but in some ways it is the natural state for a group-identity-first view--if group identity matters more than everything else, why not gather all privileges for your own group?

And this is why I fundamentally disagree that the founding principles were flawed. They have, at every turn, been used to argue against #3, and often successfully (even at the cost of civil war and considerable social upheaval). The conditions and laws and actions were all flawed at the time of founding, including some of the specifics in the Constitution (since repealed by amendment). But we have two and a half centuries of those principles being among the strongest arguments for change towards more equitable laws and society.

How else do you understand the fact that #3 is so far from reality that we don't even consider it is a serious possibility?