The design and engineering activities involved in solving this would be very enjoyable work, and the human benefits when (eventually) operational would be huge.
Every solution would need to be custom for its city/region, but one of the common ideas is concentric circles of trains, spaced at appropriate(ly large) distances, with trains running between in perpendicular direction. Basically wheels and spokes.
The wheel trains could stay in motion always, only slowing at connection points where the perpendicular trains would temporarily turn and run in parallel. Both trains would slow, cars would connect, passengers would come and go, and then trains would separate. Perpendicular train curves back in for its perpendicular direction of travel, and "wheel" train picks up speed and heads for the next spoke connection. Obviously any problem causes the joined trains to slow, even to a stop if necessary (to prevent human harm).
There are so many different possibilities here, but ultimately I think it should be possible for a human to walk 5-10 minutes to some station, get on some people mover, and eventually get out of another people mover within 5-10min walking distance of their ultimate destination... all without ever setting foot outside of a train aside from start/end points.