Three positions are held simultaneously by serious scholars and none has displaced the others: the rite as the preserved structure of a hunting kill with its attendant guilt, the rite as a system of cooking and distribution that fixes the human place between gods and beasts, and a critique arguing that the tidy opposition between sacrifice eaten and sacrifice burned entire is a modern schematisation the evidence of hero cult does not support.
What would resolve this This is not a question a single find will close. What moves it is the accumulation of excavated faunal assemblages from sanctuary deposits, which record what was actually burned and what was butchered and eaten, tested against the literary schema rather than read through it.
OpenGreek religion, zooarchaeology of sanctuary depositsRobert Parker, Miasma: Pollution and Purification in Early Greek Religion