The problem with your logic is that if you have a bow that is shooting a 500 grain arrow at 200 ft/sec it will not shoot a 300 grain arrow at 320 ft/sec. it will only shoot it at 244.9 ft/sec which is a drop in KE of 4.4 ft/lbs.
Excellent point , and it is the one parameter , that some on this thread are not taking into account .