I'm in a similar situation, only one-way out of LAX.
We're flying from DTW -> CDG in mid-September. Our plan is to arrive at DTW around the afternoon, check into the HI Detroit Metro and have some dinner and a rest before the long haul.
After pricing that route and our ideal time on ITA, it was a reality check for me too.
However, I found an AA flight that didn't blow my mind - 2 pax, 1 stop, arriving at 4:30 for $404 total. The site said there were "only 2 left at this price" - would it be a good idea to jump on this fare? I'm not sure how much I'm willing to gamble that the price will drop, considering our lack of flexibility.