I still either don't see why you say that, or don't follow what you are trying to say. The Born rule is a fundamental feature of all quantum theories, and I do

I still either don't see why you say that, or don't follow what you are trying to say. The Born rule is a fundamental feature of all quantum theories, and I don't see why Everett is an exception. If you want an intuitive picture of what the squared amplitude means, it seems that it would suffice to think of it as the fraction of phase space which evolves into the configuration associated with that amplitude.