I did a similar trip, Europe through Asia, and I applied for everything on the carnet and left the deposit before I left and then had the carnet issued several months after I left. The carnet was sent to me in Central Asia. I was on the road for a while and didn't want it to expire before the end of the trip so I wanted to maximize my time.
If you have it issued several months prior to actually needing the carnet, you will be wasting the time on the carnet through countries that don't require it. You will not need the carnet until Pakistan, so I would have it have it issued as late as possible and have it sent via DHL or FedEx to someplace close to Pakistan.
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