Interim update:

Not resolved yet, but CX/MPC does seem to be trying hard and keeping me posted (had called and sent in a polite yet firm email that elicited a response from a high-up sounding ranked person).

They've issued the ticket with the problematic segment in coach for now, so that LAN does not cancel the other sectors that they had managed to get back.
(I got concerned when i saw ticket numbers on the LAN site for the downgraded booking, thinking that CX was just trying to stuff that down my throat).

Seems to be requiring coordination with LAN via CX US.

They are also exploring alternative routings that would fit our overall itinerary (get GRU-LAX somehow since LIM is just a transit point), with a promise 'if the miles required are more, we will still charge you the same'.