The Clinton Global Initiative Annual Meeting took place on September 23-25 2012 and Obama "spoke at the Clinton Global Initiative Annual Meeting about his administration’s efforts to combat human trafficking and made it clear that the United States will continue to be a leader in this global movement to fight modern slavery."

Alefantis stayed in the White House from Sep 26 at 5.36pm (his appointment was at 9pm) to presumably some time in the morning of Sep 28 as his appointment finished on Sep 27 at 23.59 which is how the WH covers-up people staying overnight: http://i.imgur.com/Ia1lLQK.png

According to this he met with Monica Lee (ML) together with Christopher Moukarbel, Christopher Cunningham and Chelsea Swanger; respectively WH Press Assistant, a filmmaker already connected with Alefantis, a viral video blogger and porn actor, and a professional photographer.

Then on September 27 at 12pm there was a "White House Google+ Hangout to learn more about the Obama Administration’s efforts to combat human trafficking at home and abroad." https://www.whitehouse.gov/blog/2012/09/26/join-live-video-chat-combating-human-trafficking

The Hangout was composed by: "Assistant to the President, Chief of Staff to the First Lady and Executive Director of the White House Council on Women and Girls, Tina Tchen, Special Assistant to the President and Senior Director for Multilateral Affairs, Samantha Power and leaders from the NGO and faith communities who play an important role in the global movement in the fight against modern slavery. Joshua DuBois, Special Assistant to President Obama and Executive Director of the White House Office of Faith-Based and Neighborhood Partnerships will moderate the conversation"

Ideas:

Try to find cases of missing children around those dates

Investigate all the people in the hangout and their links to Alefantis

Investigate other visits of Alefantis around this type of events

EDIT - here's the Google Hangout video: https://www.youtube.com/watch?v=SF0jum-bS8Q