You need to check he can't slip down in the sleeping bag - his head needs to be bigger than the neck of the bag. So long as that's the case you can place him anywhere in the cot, the length of bag doesn't matter.
My 7 week old has two Grobags and a Tu bag - I don't put him in the Tu one yet as the neck is quite stretchy and it doesn't have popper adjustable armholes. He's fine in the Grobags though as they're not stretchy at all and have armhole poppers. He's 60cm long and 11lbs+ if that helps.