Welcome to FT! (And watch out for double posting - a no-no.)

AA regards Easter Island (IPC) as being in the Southwest Pacific for award purposes, while BA regards it as South America.

So for your AA miles, you'd need either to make it two "all-partner" awards, N. America < > S. America and S. America < > SW Pacific, for which you don't have sufficient miles, or else an AA "Oneworld" award, which requires two OW partners in addition to AA (if AA is used at all) per itinerary. Oneworld awards are mileage-based while all-partner awards are continent/region-based.

To use a Oneworld award you'd have to include a second OW airline; the easiest would be Mexicana. So an eligible route would be something like SFO LA LIM LA IPC LA SCL LA MEX MX SFO. That's around 15,000 miles and would fall into the tier requiring 130,000 AA miles for business class.

For BA, I believe you're only allowed one stopover per direction, so you'd have to make IPC your turnaround point, and use LIM and SCL as your stopovers, making your own way to CUZ. However, check the mileage requirements with BA when more than one partner is used, or else you may have to travel on separate itineraries, one person using Lan and Mexicana, the other using only Lan.