As the nominal head of ‘the bureaucracy,’ the President should be able to move at the speed of light. However, when the courts and/or the Congress get involved, we’re back to moving at the speed of smell.
The only way to dramatically change bureaucracies is to change the outcomes expected from them. You will never win an internal fight over the processes bureaucrats are using or the traditions they are following. The bureaucrats will simply slow walk you with more and more arguments and information.
The key is to instead figure out the positive, measurable outcomes you want and insist on the bureaucrats changing their system until it can produce to your expectations.