I'm not sure what it would take to shoe-horn the later engine and tranny into the 56 Fury, but I would not tamper with the 303. It is worth more as an historical engine than you would ever get from it if you modified it beyond restoration.
I restored a 56 Fury and made great effort to keep everything as it came from the factory. I am proud of the results. I have seen 56's that have been beautifully modified, but are not far from stock. Bigger engines were not part of any modification that I have seen since the entire drive trane is not capable of handling much more than factory original i.e., suspension, brakes and overall design of the car.
Start the year off right. Easy ways to stay in shape.