The easiest way to circumvent this and other problems with poweron, power off is to just put a simple three pole switch on the white accessory lead that wakes your PC up.
You have three wires running to the PC, ex. red (constant power), black (ground) and white (accessory) power (only on when ignition on).
Run the white wire from your accessory power to the top leg of the switch.
Run a red wire from the constant 12V power to the bottom leg of the switch.
Run a white wire from the middle leg of the switch to the white wire going into your PC.
With the switch in the top position, PC works as it does now, starts and shuts down when power on accessory is seen.
With the switch in the middle position, PC doesnt start. This is where you put it to just start the car and move it.
With the switch in the bottom position, the PC will stay on and running even if you shut the engine. Good for quick stops when you dont want to go through a whole shutdown/wake up from hibernation.
The switch also acts as a reset switch for when the PC hangs or something doesnt initialize right, switch to middle position will cut power to the white line and the psu will do a shutdown, flip it back to top position and it will wake up.