“There are numerous inscriptions naming and linking Anubis and Roustau (the Sphinx).”
Ah, but as you said in an earlier comment, “Rostau” is not a name for the Sphinx. “Rostau” is a name for the whole complex on the Giza plateau, which is a symbolic representation of the underworld, and thus the connection with Anubis can be made regardless of any association with the Sphinx. The Sphinx itself seems to be linked more closely with Horus (Her-em-akhet) than with Anubis, and Horus was indeed often depicted with the characteristics of a lion.
The Monument at Rostau was a jackal headed monument crouching as canines do, looking to Canis Major and Sirius rising guarding the Land of the Dead, associated with Anubis.
Everything else came later especially after Herodotus. The body being interpreted as a lion, when it obviously is not.
It likely far predates the Old Kingdom and the later re-carving of the head with the added legends of a lion and Leo because Cains Major no longer rose in the East.
Sirius makes more sense than Leo in the tales of Osiris and Isis, where there is no Leo. Your mileage may differ.