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My guess is that as long you require the inner product of an atomic idempotent with itself to be normalized, that the inner product is unique. This probably follows in some way from the classification theorem for Euclidean Jordan algebras.
It is true if you restrict $A$ and $B$ to be upwards-directed sets. This is essentially because of Kadison's characterisation of von Neumann algebras as being directed-complete C*-algebras (with a separating set of normal states). Hence, we can just take $z$ to be the supremum of $A$.
