Unfortunately, I think you're SOL on earning AAdvantage miles. The AA site mentions no mileage earned on BA transatlantic flights. The oneworld site states, "American Airlines AAdvantage and British Airways Executive Club members can earn and redeem miles, and earn tier status credit, on all eligible flights except each other's routes between Europe and the Americas."

I could understand the application of this rule for flights to North America, but to include Central and South America in the scope of applicability is absurd.

If you really want AA miles, want to avoid MIA and can travel on a Monday or a Friday, you can take LX from LHR-ZRH-GIG via GRU. LX First is quite nice. Obviously LX isn't an option on a oneworld RTW. Hopefully, things will be different in the future.