The way you have S1 connected, there never is a voltage from V1 applied to the circuit.
S1 should be moved to just in front of Vout.
Why did you move the switch's position from that shown in post #13?
Also the polarity of S1's control input is reversed.
As connected, S1 will be off when U1 is on (high battery voltage condition)..
A P-MOSFET, connected as shown in post #13, is ON when its gate is pulled to near ground, and OFF when the Gate is near its source voltage.