I found the answer to my own question in the end. Thought I'd post in case anyone else has the same situation.
Turned out to be very straight forward. I went to the aduana office in Osorno where I happened to be, explained my situation and 15 minutes later walked out with a duplicate. I didn't even have to produce my vehicle docs or police report, but that may have been down to the very laid back chap in that particular office. I've had a few reasons now to sample Chilean bureaucracy and would guess other aduana offices may want to see both docs.
I seen a number of aduana offices in various towns, so if you have a chance, find a small quiet one and avoid the queues.
Don't know if you could do this at the Aduana at a border crossing - didn't want to try it and get turned back.
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