LH F was a stretch this summer, waiting to see what i get hit with for the JFK-LAX-SFO-HND F on AA and JAL for an infant. I may have to leave my kid sooner, or just MS a bit more to pay for it.
LH F is pretty easy, since M&M only charges $17.2 for an infant.
JFK-LAX-SFO-HND F on AA and JAL, you can book one with AA and one with BA to add the inant, still a little expensive but doable.
OT - I'm looking to go to Israel with BA on BA metal with a CP. Comes out to 99k and around $1000 for 2 pax and infant in F OW.