Why wouldn't my latching switch circuit turn off?
When you push the switch in order to toggle the circuit off, Q2 is closed as long as the switch is pressed and C1 is charged, whether Q1 is 'biased' or not.
I guess your LEDs behave capacitively?  

That would explain that Vout doesn't 'immediately' return to zero, but that R5 takes some time to discharge the capacitance in the load, which however at the same time will charge C1 through R2.
Your reduction of R5 speeds up the discharge, but increases the power dissipation in the on-state.  

Maybe an increased (doubled) value of C1 would give the original R5 more time to discharge the load's capacitance.