Why exactly can't a SERIALIZABLE transaction use the index it created itself? If you add a pointer to the root of all HOT update chains where either the HEAD is alive, or some tuple is visible to the transaction creating the index, shouldn't this be sufficient for using the index in the creating transaction?
Tuples in the HOT-chain may not share the same index keys with respect to the new index being built (they share the same keys for all existing indexes though). So we don't know which index key to use while building the index.