You could try running the +12 volt lead dierectly to the battery, and as was said before, gring a spot on your car chasis very clean, right down to shiny metal.
At least if you do that, you can say that you got power right from the source.
But be sure that you route the + 12 volt and ground so that they do not come near ignition wires or wiring for car elctronic control unit, as both can be very noisy, and could induce into your monitor power wires.
You may need to buy an alternator noise filter that connects directly to the alternator +12 volt output.
I have had a problem kind of the opposite: when I use the manufacturer supplied cigarette lighter plug adapter (with built in noise filter), the monitor itself induces noise into my audio system...
I run an inverter in my car, so I just used the monitor 120 volt ac adapter and plugged that into inverter. Even then, there is a verrry tiny whine in my audio system when monitor is turned on. not loud enough to worry when music is on.
Happy CARPC'ing!