In general it's clearly possible, but you will have to refine some of the details. For North America you are basically restricted to the routes operated by AA, for South America LA and LP. I doubt you can fit all your Mexican and Brasilian destinations into a OWE. As for your "return," somthing like

BUE-SYD-MEL-AKL-SYD-TYO-HKG-BOM/DEL-HKG-LHR-TLV-LHR-YYZ

would work. You can also add two Asian and two European segments to get more mileage.

Speaking of mileage, what FF programme do you plan to put the miles in? If you want AA miles, for example, you need to avoid BA transatlantic, which means LHR-YYZ nonstop is out.