I am also worried about the whole LAX terminal transfer thingy with an infant + carry on bags. Getting out of T7, and transferring to TBIT at LAX, seems like a hassle (specially with a toddler). Am I too worried about this?
I don't believe that you are "too worried" about it. I think it is a reasonable concern. If you had no other option than to transit through LAX things would be different, but considering you have the option of avoiding LAX, I would do so.