Not completely sure this would help but its a thought - VFR under Bravo in the direction you need until you can climb under Bravo and eventually pick up your clearance that way. Even if you file IFR from the ground, sounds like you might end up copying a new plan that takes you in the wrong direction until you fit into the traffic flow from what you posted.
So, possibly taking it easy on the fuel flow, flying low under the space as a plan at first? Passengers love the city lights from those low altitudes
