Thank you all for your contribution. Things are a bit clearer now.
I have a feeling I might have to go for a cash booking for the sectors to and from ICP. Tickets are pricey, more than $600, but business is not much more expensive and, considering the TPs and extra Avios, it won’t be too bad.
I have also noticed that MDZ-SCL-CJC comes up much cheaper when priced as a return rather than one way. AEP-MDZ, instead, has ok prices as a one way.