As far as I'm aware it's not permitted to overstay the TIP or CdP time limit without some type of force majeure justification. I suggest contacting the DIAN and asking about putting it in customs bond somewhere.
I know that people have closed their TIP/CdP at the Ecuador border then returned and parked bikes/vehicles for long periods in Ipiales. Obviously I can not recommend something which is illegal.
The other question is whether/how to keep the bike outside Chile for this period without contravening the rules.
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