Using a MOSFET to turn on/off LEDs which could get reverse voltages
Use TWO MOSFETS in a "back to back" configuration to form an effective single FET with no body diode.

Connect source to source, gate to gate.
Name one drain DU = Drain upper.
Name other Drain DL = Drain Lower.
Consider DL = source of the MOSFET pair.
Consider DU to be drain of MOSFET pair.  

In this diagram note that M2 drain and source are swapped compared to "normal" usage.  







simulate this circuit &ndash; Schematic created using CircuitLab

Place LEDs in MOSFET Drain circuit (between DU &amp; R1)
Connect DL to ground.
Drive two-gates (joined) as input.
(MAYBE a say 1 megohm from joined sources to ground - try without it first).

Report back.

This works (we hope :-) ) because a MOSFET is a 2 quadrant device.
As long as Vgs is positive then the MOSFET will conduct in either direction.  

Simulation MAY not want to turn the pair on without the 1 megohm mentioned above.
Real life usually will.