Below is the LTspice simulation of DD's basic circuit in post #5.
It removes power to the load with the circuit staying connected to the battery which draws only about 1/4mA.

R1 is a lower value so the TL431's quiescent current doesn't turn Q1 on.
Q1 was changed to the PNP 2N3906 (the 2N2222 is an NPN although shown as a PNP).
There is a little over a volt hysteresis from the turn-off to the turn-on point as determined by R4.

View attachment 272267

Is there any way I can reach the SPDT model you used? I couldn't find it anywhere myself..

 

Look here.

 

Look here.

Thanks a lot!