LAN is a tough customer when it comes to RTWs (okay, they are tough on the customer). I have no tried to get AKL-SYD, but did have luck getting SYD-AKL in F using the QF flight number. SCL-USA flights and vice versa can be tough, but trying the AA code share is good option.

Has anyone done FRA or MAD-SCL in F or J on LAN as part of a RTW?

I have had a much easier time on all other airlines. CX, BA and QF are, in my experience, pretty easy.