My thanks to all of you who responded so generously to my query in January about the fate of the photographic archive of the Istituto Italiano per l'Africa e l'Oriente (ISIAO) in Rome. Through all of the clues and contacts you helped provide, I've found some concrete information.
The object collections have primarily been transferred to the Pigorini Museum, while the photographic archives pertaining to Asia (from the former Istituto Italiano per il Medio ed Estremo Oriente) are now at the Museo Nazionale d'Arte Orientale. All of the archives--papers and photographs--pertaining to Africa remain in the former building of the ISIAO, which is still closed to the public. As of now, there are plans to reopen the library and photographic archive, with a potential transfer of materials to the Diplomatic Archives of the Ministry of Foreign Affairs in Rome.
So we'll have to wait a while longer, but at least it seems that there is a chance of future access!