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.
UPDATE: I have some preliminary comments on the 2019 search which is described in National Geographic. I had nothing to do with that search.