In regards to Australia, I'd recommend PER-AYQ-SYD over PER-ASP-SYD. Uluru is spectacular and not to be missed, and given there's direct flights from PER and to SYD from AYQ, it's worth stopping there. ASP on the other hand doesn't really have so much to offer - it's a regional town in the middle of nowhere, and whilst there's some alright attractions in the local vicinity, none of them come close to Uluru (and the Olgas as well while you're out there).

Depending on your interests it might be worth continuing on from AYQ to CNS before SYD as well (again, there's direct flights from AYQ-CNS). While Cairns itself isn't *that* amazing (but pleasant enough), the surrounding areas are great, out on the reef, up to the Daintree and Port Douglas and even taking the train or skyrail up to Kurranda is enjoyable too. You seem to have a free segment left in the South Pacific, so certainly worthwhile using it while you're down here.

In South America there's flights available on Lan Peru from LIM-GRU now as well, if you're wanting to get from Lima to Brazil before heading down to Argentina, but unfortunately nothing that carries all the way through to Rio.

Keep in mind also that the rules now let you travel through the point of origin as part of the RTW ticket (though you're only able to leave the country once). So if you had a domestic UK destination you wanted to include as a second stopover in the continent of origin to enjoy at a later date, you can do that as well.