I'd change up the order of your trip and try to avoid the EU during August. I'd try to use a RTW flight and then intersperse round trips on separate itineraries. You will need a few positioning flights and strange routings once in a while but this can be done.

My order would be EU in spring making sure to hit Eastern Europe. I'd jump to SE Asia and then on to Oceania and Australia. Finish your trip in South America and Central America. I haven't done a trip like this since I'm all corporate travel but that's my instinct.