I couldn't find a 600k trimmer resistor but I ordered a 500K and a 1 meg.
The trimmer in my circuit
is 500k, not 600k. (Sorry if the image wasn't clear). The 470uF will be fine (giving slightly longer LED fade-in/out times than the original 330uF)
I wouldn't recommend trying to boost the AAA voltage to run the LED array; battery life would be very short. My circuit is designed so that the AAA cells power only the PIR (hence have a long life) and a separate external 6V source powers the circuit and the LED array. The voltage needed to trigger my circuit is anything from ~1V to >50V and the current drawn is negligible (so 3.6V from the PIR is fine).
Circuit operation is as follows:-
A positive-going pulse from the PIR turns on Q1, pulling the Trig input of U1 (the 555 IC) low. This starts the 555 timer running and U1_Out goes high (6V). C2 charges up via R12. When the C2 voltage reaches ~4V (as sensed by the U1_Thrs input) the timer stops, U1_Out goes low (0V) and C2 discharges quickly via U1_Dis. Thus the timer is reset.
While U1_Out is high C1 charges up via R10. The rising C1 voltage drives the gate of the FET (M1). When the gate-to-source voltage Vgs exceeds the turn-on voltage Vt (~2V depending on FET type) the FET begins to conduct and current passes through the LEDs and R13. The voltage developed across R13 by the current raises the FET source terminal voltage. The result is that with increasing C1 voltage Vgs is held at Vt and the FET (and LED) current increases too, thus giving fade-in. When U1_Out goes low C1 discharges via R10, R11, D15, giving fade-out. Trimmer U2 and D16 allow a bias voltage of slightly less than Vt to be applied to the FET gate and prevent the C1 voltage dropping below Vt (except when the circuit is initially powered up). This ensures the fade-in starts as soon as the PIR triggers the circuit. The trimmer should be set so that the LEDs
just turn off fully.
How much voltage will be put to the LEDS? I will need to size the resistors to the LED board
You don't drive LEDs with voltage; you drive them with current. As shown there are 7 strings of LEDs, each string having 2 LEDs. The current (~22mA peak) in each string is the FET current (~150mA peak) divided by 7. R3-R9 are present to allow for manufacturing variations in the forward voltages Vf of the individual LEDs and help to balance the currents in the strings.