At a guess, P-AO9, pin 6 = Standby 5V (stable), pin 9 = Power-On (stable), pin11 = BL-ON (all over the place).
P4, pin 3 = BL-ON (all over the place).
LD3, pins 3 and 9, LED supply volts, should be stable.
Suggestion: cut the lead going to pin 11 of P-AO9 in a place where it can be resoldered later on. Make sure all plugs are in place. Then place your resistor between pins 6 and 11 of P- AO9. Now you are controlling the backlights, not the A-board. If pin 11 is now stable, then the A-board is causing your previous fluctuations. If the backlight don't light up, I'd say you have dead LED/LEDs in the display panel - LG panel, is it? Quite common.
Don't suppose you have a LED tester? My guess is based on the voltages you have supplied and may not be accurate. Good work on your attachments.
Bruce