Even if the electrons move slowly, it can remain true that it only takes a few ns for them to settle down. The time for any of the "wrong paths" to have their c

Even if the electrons move slowly, it can remain true that it only takes a few ns for them to settle down. The time for any of the "wrong paths" to have their current drop to zero after the switch is thrown will be determined by the RC time constant of that path, where C is the stray capacitance and R is the path resistance. That's going to be over pretty quickly.