In my universe the Green Lantern Corps would have always had at least two Lanterns per sector. I would have Hal Jordan be the first Green Lantern from Earth after the death of Abin Sur. I would start out Sector 2814 with Hal and Amon Sur as partners. Amon Sur would be one of the first deaths during the attack from the Greek Gods (see How I would do it Justice League) and after that he would be replaced by John Stewart. Some time after John and Hal had worked together John would be badly injured and would be replaced by Guy Gardner. When John recovers from the Guardians would thank Guy for his service and offer him a spot as honor guard. Some time after this I would have Hal die in some event (probably my version of Doomsday) and he would be replace by Kyle Rayner. After that John would take Hal's spot in the Justice League and Kyle would join another of earths teams (probably my version of the Titans).