Regarding your second point, AA.com isn't going to show availability between LHR and CDG, IIRC, because they don't fly that route. For OW availability, I use BA's site.
This really doesn't help you, because its still a bunch to get across the pond, but its good to know.
In terms of getting across the channel, just so you know, there are flights (in gasp, coach!!) for under $100 on 7/6 direct to Paris (try area airports). Obviously, it depends if you and Mrs. David are the type where flying is the fun part or not.