Well I respecfully disagree. Some of the destinations (Easter Island stands out) are not easily visited with one-way or local tickets (and IIRC not the Lan pass either.) In general the addition of S. America works against such make-it-up-as-you-go plans, but YMMV.

While it's true that LONExs are well priced ex-UK, the no-transit rule hurts where LHR is the origin airport.

But note that Finland is (according to WBT's spreadsheet) only a couple hundred dollars more for an LONE4 than the UK, and in fact AY's (unique in OW?) route to CAN helps with the OP's itinerary. There are still several open segments where either there's no OW service or not enough continent coupons for the whole menu, but these can be covered relatively easily with one-way tickets or even trains/buses.

For instance, the following hits most of the OP's spots, with one or two surface/S. America pass or OW tickets added:

HEL-CAN//PEK-HKG-DEL//BOM-BKK-HKG-xLAX-LIM-SCL-IPC-SCL-USH//EZE-JFK-WAS-LAX-LHR-TLV-MAD-ATH-HEL

AY's service from ATH to HEL is seasonal and on all-Y config. planes, but so what? USH-EZE is around US$300; I'm assuming the OP could make his/her way overland from DEL to BOM to connect to the BKK flight, etc. etc. I also made up the N. America itinerary; numerous riffs possible. I'd take the train from NY to DC myself, rather than Eagle or fussing with airport hassles.

It's a lot of real estate for the price.