One thing that pops into my mind immediately: decoupling capacitors! Those LEDs draw a whole lot of current and those two little electrolytic capacitors are like a drop of water on a hot stone. I don't see much capacitance next to the local 3.3V regulator either. You might be suffering from brown-out resets. Have you measured the supply voltages with an oscilloscope yet?
I'd try enabling the PWM with the LEDs or the DC-DC chips disconnected, or use a 2nd ESP8266 with a small LED as a heart-beat indicator and see if that resets as well.
Regards,
Robert