Could they not arrange for road transport of the organs to CHC to meet the aircraft as it lands?
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Depends where the organs are.
If it is in location other than a major city, the retrieval team travel on the outbound flight and conducts the recovery of the organs which can be up to 6 hours for a heart retrieval.
They then fly back on the aircraft and then do the transplant operation.
If the organs are in a location where the local surgeons have been trained for organ retrieval, you may only have to pickup an esky.
Contrary to popular opinion, crews on Private Ops also suffer from fatigue
Sure, but sleeping on makeshift bed in a spare office at the airport or in the aircraft for 6 hours does reduce the fatigue.