What happened last autumn?
Now is spring in Santiago and I see some crispy brown leaves in your first photo. You say obvious root problems. It could be. I suspect a pathogen causing the xylem to become clogged. A fungus that entered via a wound is usually how it happens.
If so, follow all the branches with crispy brown leaves back to a common point OR a point where the leaves are no longer crispy brown --> do you find a scar/wound? Usually the fungal pathogen gets introduced because the cutting tool was inoculated when it was previously used on a diseased tree --> you should sanitize your cutting tools after use, if not before use.
So, you're looking for something like a point where you lopped off a big branch or, say, made a partial saw cut like one might do with approach grafting. If this fits with you. If this is the pattern you find, the remedy is to (sanitize you cutting tool before) remove the branch at a point below that entry wound.
If you don't find a wound associated with any of this, then it could be a root issue. With any luck, it will be only one side of the tree --> the roots on that side are the ones that are dying for some reason. There are bacterial root pathogens as well as fungal ones. A hydrogen peroxide drench might be effective. I buy 3% peroxide at the grocery/pharmacy and dilute it to 1000 to 3000 ppm (0.1 to 0.3%),
What are your observations in these regards?