This site presents a viable theory that Mallory and Irvine summited Mount Everest on June 8, 1924. They climbed a moderately difficult route just above the Couloir (pictured above) which had been identified by E.F. Norton two days earlier. They did not climb the Second Step, but instead took a lower route to bypass the obstacle, just the way Mallory described in the 1921 reconnaissance report.
Mallory described his potential route to John Noel, the 1924 expedition photographer, in the days prior to his climb. Mallory stated his first route choice was to go up the Couloir to access the north-east section of the final pyramid. His backup route was to cross above the top of the Couloir and access the ridge of the East Face at a point above the Couloir. It is this second route that matches with the sighting of Odell at 12:50.
Mallory and Irvine reached the summit and died on the descent from a fall in which exhaustion, dehydration, and hypoxia were all contributing factors.
UPDATE: I was at Mt. Everest in 2018 but the snow coverage was too much and it was not possible to get to the ledge safely. I will post some information about Mallory’s route as time permits, but no additional information is available about the location of Irvine.