Another idea would be to let people/companies/organisations lease large areas where they had a fishing monopoly. Then they would have an incentive to maintain strong populations to secure big future catches which only they would have access to. As fishes move around, these areas would need to be very big. Peak oil is not an energy crisis. It is a liquid fuel crisis.
The lease idea wouldn't work because the usual Market Bollocks would reward short term performance over long term husbandry, and strip-fishing would earn more than long term fish management.
Once the owners run out of fish, they can always move to something else, like blowing the tops off mountains for coal.
The fact that the fish would remain extinct wouldn't be a problem for them.
The most, and may be the only practiceable point for control is the ship (e.g. the number, size and technology allowed). This calls for traditional command and control policy.
We should be shredding a lot of the larger ships.