Conjecture?? What? Do you expect the Klingon mythology to be depicted onscreen? It's fiction within fiction!
From the DS9 epsiode "Homefront", where Worf and Kira are discussing their respective beliefs -
WORF: Our gods are dead. Ancient Klingon warriors slew them a millennia ago. They were more trouble than they were worth.
Klingon mythology says they had gods, and then killed them all off. Who will be the spiritual authority of Sto Vo Kor, then, if not the gods, since they're dead? Presumably the Council!
If you're a Klingon warrior, and believe in Sto Vo Kor, then presumably you'll listen to the authorities about what it takes to be granted entrance to Sto Vo Kor. Who but the Council would be the leading authority on the afterlife?