carbon forging is very strong and highly impact resistant the similarity with chopped mat ends when you take into account what actually happens to the fibre in the forging process ,it will cost you 10s of thousands in tooling however to achieve properly but car suspension wishbones are manufactured using this process
Don't think of composites as a metal part turned into carbon fibre ,thats the biggest way to misuse carbon fibres properties ,i would mould that and lay fibres according to how energy you wish to store then release from the bow ,this is most likely to be unidirectional fibres and containment plies around them ,think along the lines of muscles in the human body