There is 0 chance of D inventory opening up on JFK-SYD. They save it for oversells when it is down to 0 and some cancels occur. Your best bet is to reroute SCL-LAX-SYD or even SCL-SYD (which is a more comfortable trip, fwiw). I guess your other choices are what Viajero has suggested, or to buy a surface segment (JFK-LAX). You have to have a legal transit in NA, which means less than 24 hours (and in the past surface segments were also not allowed, as they were considered to be a stopover).

The cancel button is quite potent on aa.com, I've canceled a few reservations by mistake when my mouse missed by 1, and the confirmation screen before the cancel is really not useful (as it doesn't provide the routing to identify your reservation). I've learned to name all my reservations on aa.com rather than leaving it the system generated name, which helps a bit with this problem. I've never seen Sabre make a mistake in the history of the reservation, so I'm sure it was from your computer.