I heard a story about Baba's portrait being taken to Shirdi. Who was actually involved, and where did this happen? I thought it might have been at Hemadpant's house.

According to Chapter 51 of the Shri Sai Satcharita, the individuals who took the portrait to Shirdi were Madhavrao Balwant Deshpande and Kakasaheb Dixit. This event did not occur at Hemadpant's house, but rather at the house of Kakasaheb Mirikar. The portrait was already at Mirikar's home because it had been sent from Shirdi for repairs after its glass had broken. Balasaheb Mirikar, who was holding onto the repaired portrait, entrusted it to Madhavrao to take back to Shirdi. Dixit, who was also present, was overjoyed at this fortunate occurrence, and the two men set out for Shirdi together with the sacred image.