You would be surprised at the number of companies who do mixed mode operations like this. Keeps the aircraft flying and earning revenue. It is not the Skydiving clubs that operate under an AOC it is the company that operates the aircraft and leases them out to a variety of purposes that will hold the AOC.
Operating under an AOC allows the operation to choose the work they want and stay strictly within the law. Some are also approved type rating training organisations as well.
The BPA specifically recognise that many parachute aircraft are operated within AOC ops.
5.8. Pilot Fatigue.
A pilot who is engaged in parachuting operations should not fly more than four hours
without a thirty minutes’ break away from the aircraft, and should not fly more than
eight hours in any one day. Air Operators Certificate (AOC) holders should normally
continue to apply the flight duty and rest period limitations associated with their
AOC operation. In addition the flight time limitations prescribed in Article 65 of the
ANO are applicable - 100 hours in any 28 day period and 900 hours in any one year.