I flew my family of 4 to Europe in the summer four times: 2005, 2007, 2009, 2012, all at the low level award. We were always on the same flights. All segments were in J, with one exception of LHR-SFO in F. Used AA miles for everything except one 1-way SFO-FRA-HAJ on LH.
Been lucky so far. I hope I can do it again.