PWM (Pulse Width Modulation) vs DAC (Digital Analog Convertor)
It seems you have two problems. The first is that the low pass filter. The 1k resistor is out of place. The micro is able to charge the capacitor though the 100 ohm but when micro swings low it just discharges it though the 100 ohm faster then through the 1k to the level shifter. 

The second problem is the level shifter. Unless it is a special linear kind they normally only do digital outputs. The low pass filter on the input to a digital level shifter is pointless and can cause problems with the level shifter. Try placing the low pass filter between the screen and level shifter.