Ok, so your big plan for quadrupling the speed of the tube is for trains to breeze through most stations without stopping. It's like amputation as a weight-loss tactic.
Simulate it and see... The vast majority of journeys become quicker, even though many trains don't stop at many stations.
The optimal strategy is probably to have multiple express routes - ie. Train 1 stops at station A, C, E, and train 2 stops at B, D, and F. A better signalling system becomes necessary for that though - moving block signalling isn't sufficient - you need one that can take into account velocity-acceleration-jerk of both trains to get trains close enough while still ensuring passenger safety. That in turn requires Comms systems not just train presence information.
The optimal strategy is probably to have multiple express routes - ie. Train 1 stops at station A, C, E, and train 2 stops at B, D, and F. A better signalling system becomes necessary for that though - moving block signalling isn't sufficient - you need one that can take into account velocity-acceleration-jerk of both trains to get trains close enough while still ensuring passenger safety. That in turn requires Comms systems not just train presence information.