I finally beat it. I played this way more than I'd like to admit, and strangely enough, I never got the 2nd baby giggle ever until I decided to stream it.
The first thing I figured out before I started streaming was that I could make the 1st giggle happen on cue. I thought it was when I did a few things and then walked right to the phone, but after reading here it looks like it's the 10 step trick:
http://www.twitch.tv/supremestarhawk/c/4901308
Then, while streaming, I got the 2nd giggle for the first time ever, only to lose the fucking thing:
http://www.twitch.tv/supremestarhawk/c/4901201
I think it was because I moved, but I'm not sure. It was like the vibration in the controller just faded away.
I kept trying though, and right when I was about to quit, I got the 2nd one again. Also, watch me freak out about walking through the door and looping again after getting the phone call
http://www.twitch.tv/supremestarhawk/c/4901255