Normally, if a basis is regarded as ontologically fundamental, it is because all one's worlds are basis vectors in that basis. "Alive plus epsilon dead" and "dead plus epsilon alive" are definitely not basis vectors from the position basis.

Anyway, the important fact is that for Robin's scheme to work, each individual world must have small amplitudes of other configurations shadowing the dominant configuration. It's a sign that it's a contrivance, that it doesn't work. Do the small-amplitude copies of me in other states that shadow me in this individual world also have experiences? If so, doesn't that screw up the reproduction of the Born probabilities? Because that is all about just counting the dominant configuration.