This problem does not have anything to do with the "filters" (in this case L2200 & L2201) IMO. The backlight works, the LCD is being driven...and you have tried 3 different LCD's. Do they exhibit the exact same problem or just problematic in general?
The LCD image is directly driven by the CPU and goes directly to the logic embedded in the LCD. Other than some common mode chokes (L2222 etc. - there are 5) in between the two, there isn't much there. I would check the connectors on the logic board to be certain they are not cracked or damaged. I would also test the chokes to be certain they are letting the data stream through. If you had access to a known-good LCD or another mini to verify those you have, then you could start eliminating some variables.
Let me know what you find, it might give me some other ideas.