I'm convinced the aunt's experiment is to shape Minamoto to be her ideal lover as a "Hikaru Genji" copy.
This is from the wikipedia:
"Genji adored his stepmother Lady Fujitsubo (藤壺), a later favorite consort of Emperor Kiritsubo, because of her close resemblance to the dead Lady Kiritsubo, and that similarity was also the reason that Emperor Kiritsubo had her enter his court. As a result of Fujitsubo and Genji's forbidden love, she bore a boy, later Emperor Reizei (冷泉帝), to Genji when he is 19, but almost no one knew the truth of his birth, and the child was raised as a prince and son of Emperor Kiritsubo."
The aunt, Kaoruko, is Lady Fujitsubo. Why? Most likely because she was hurt/disappointed by a man and idolizes Genji to an obsessive point that raised her expectation of love too high.