Is it just you?

Sequencing/Timing wise two things are key. First AA flights must be booked before devaluation as noted above otherwise this won't work. In addition AA off peak Y is only eligible October - May 15th.

If it were me this would be the ideal:

USA - LHR (AA Y, 20k AA)
London to Paris (Train)
CDG - HND/NRT (QR J or JL J, 52.5k AA)
HND/NRT - BKK (CX Y or JL Y, 10k AA or 20k for J)
BKK - SYD/AKL (TG J or NZ J, 30k UA or 40k for F)
SYD - AKL or vice versa (Buy it, cheap flight on VA or Jetstar)
SYD or AKL - SCL - GIG/GRU (QF or LAN J, 50k AA)
GIG/GRU - USA (UA, 55k UA)

Grand Total: 132.5k AA miles (assuming you can get 2.5k AA) and 80k UA miles (or 90k if you use F from BKK - SYD). That'll leave you some extra miles to play with for flights where I suggested using train or buying. This also puts you in J for all major flights with USA - Europe in Y (which I tend to think is sufficient if you are coming from the East Coast especially if you do off-peak Y) and TYO - BKK which is a 5 hour flight (but if you can generate an extra 10k AA you can bump that one up to J).

This all assumes you can find saver availability. You'll have to be very flexible, I have no idea if it is even possible to get seats on the QF or LAN flights from Australia/New Zealand to South America.