According to the liner notes of both Zombie Heaven and the 50th anniversary edition of Odessey and Oracle, fifty years ago to-day (10 July 1967), the Zombies recorded "Hung up on a Dream."
In full, the Zombie Heaven liner notes entry for 10 July reads: "EMI Abbey Road No 3 recording 'Hung up on a Dream', 'A Rose for Emily' (reduction master)." The entry for 11 July, the next day, reads: "EMI Abbey Road No 3 recording: 'Hung up on a Dream' (reduction master)." I'm not certain, but I'm assuming that "reduction master" means they bounced down elements so they would have more tracks available to record more parts. As I mentioned back in June, I think this 10 July session may have been when the mellotron for "A Rose for Emily" was recorded because "Hung up on a Dream" certainly features that instrument.