Here is what I think you are asking for:

cai-lhr-hel-cdg//lhr-gig//puq-scl-ipc-scl-uio//scl-akl//chc-bne-asp-drw-adl//syd-nrt-hkg-bkk-lhr-cai

This creates a few expensive open segments in South America. One suggestion would be to buy a separate round trip, scl-puq-scl. Then you would have:

cai-lhr-hel-cdg//lhr-gig-scl//puq-scl//ipc-scl-uio//scl-akl//chc-bne-asp-drw-adl//syd-nrt-hkg-bkk-lhr-cai

You could buy an extra segment in SA for the uio-scl return. Another suggestion is to reconsider going to Easter Island. Unless you really want to study the Moai statues, there is not much else there worth visiting.

Note that I have not checked that all point to point flights exist but they look reasonable.