I'm glad you have found a valid starting point.
pugabral, can you confirm that the turnout motors being used are:
If so, they advise connecting the LEDs in series with the motor, as you originally drew. This gives ~5mA drive current while changing states, and 16mA when at the limits (motor stalled). No series resistors are needed for the LEDs in this configuration. The LEDs will be dimmed during transition.
The 9VDC power supplies being used are two-prong; this means that they are isolated, and have floating outputs. Therefore, any fault condition causing the pulsating output would be due to bad wiring or a defective motor, rather than a power supply being shorted via the other power supply's connection to earth.
Can you test a single motor with LEDs from your power supplies to confirm that they are working? Use the same setup as for the batteries, where you showed it working. At least then you know the power supplies, LEDs and motor are not the issue.
In your full setup, it's quite possible you have some diodes in the wrong position.