I would certainly try another call, and if you get the same answer be a bit more direct with a supervisor about the terms I quoted above: that you don't believe BA are making reasonable efforts to reaccomodate you.
If waiting a few days suits your wife, there are 2 avios seats on IB MAD-SCL on Tuesday, not a bad way to get there. If you have an IB+ account, the best option would be to ask BA to protect your return leg and then book it yourself (150k+£174 for two, booked through IB+, so not horrendous compared to your F leg) and buy a cheap seat to UK-MAD.