As a last resort you could try tying the dead bird to his collar,at the back of his neck where he can't reach it and leaving it there for as long as you can stand it.
I did this with a chicken one of my dogs had killed(many years ago) on someone's advice.She never looked at the hens again!!
Alternatively you could keep him indoors,taking him for long walks on a harness and lead as one would a dog.
The damage that cats do is,by and large,hidden as one doesn't usually see the corpses.
I had Siamese and Oriental cats for years,they only ever went out on leads and were most contented cats.A large cage in the garden might be a good idea as well?