Europe-Asia-Southwest Pacific-South America-Europe, 4 continents - check.

I'm not a OW expert, but AFAIK

CAI-GIB no direct flights will need to go via LON
SVO-NRT no direct flights will need to go via LON.
NRT-PEK no direct flights will need to go via HKG

South American routes I'm not familiar with but as only LAN (not LAN Argentina?) some of those sectors may not be allowed

SAO (presume you mean Sao Paulo GRU?)-DXB no direct flights need to go via LON. Not sure if you're allowed to start and finish in different countries?

Only allowed 2 flights to/from LON and CAI/SVO/DXB (and several others) - appears you have more than 2.

AKL-SCL is more of a problem in first - due to extremely limited F seats at all, never mind "A" booking class. Slightly less of a problem in business but still only a few flights a week so harder to get than most routes.