Since you only want to light up 1 out of 2 LEDs, you can get rid of the voltage regulator and use a constant current source instead:
Vpower is modeled as a 10V DC source with a 2V sine rippple at 60 Hz.
D6, R7, R1 and Q4 make a constant current source. D6 keeps the volate at the base of Q4 at 4.7V below Vpower. Vbe of Q4 is ~0.7V, therefore the voltage across R7 is 4V, regardless of Vsupply. 4V/560Ω gives a current of 7mA (in the simulation we see ~6mA).
Q1 and Q2 control the current flow from Q4 to go either through LED D2 or LED D5. Q1 and Q2 in turn are controlled as in my post #4 from the 3.6V (RMS, therefore 5V peak in the simulation) Ac input.
A residual ripple on the LED current is visible in the simulation, but will, I think, be invisible in real life due to the small amplitude and the frequency (60 Hz are invisible to the human eye). In practice the ripple on Vsupply will be at at an even higher frequency of 120 Hz due to the bridge rectifier (I left out the full model for the power supply in this simulation).
Vpower is modeled as a 10V DC source with a 2V sine rippple at 60 Hz.
D6, R7, R1 and Q4 make a constant current source. D6 keeps the volate at the base of Q4 at 4.7V below Vpower. Vbe of Q4 is ~0.7V, therefore the voltage across R7 is 4V, regardless of Vsupply. 4V/560Ω gives a current of 7mA (in the simulation we see ~6mA).
Q1 and Q2 control the current flow from Q4 to go either through LED D2 or LED D5. Q1 and Q2 in turn are controlled as in my post #4 from the 3.6V (RMS, therefore 5V peak in the simulation) Ac input.
A residual ripple on the LED current is visible in the simulation, but will, I think, be invisible in real life due to the small amplitude and the frequency (60 Hz are invisible to the human eye). In practice the ripple on Vsupply will be at at an even higher frequency of 120 Hz due to the bridge rectifier (I left out the full model for the power supply in this simulation).