Plus, the available solutions all seem real cargo cult-sciency - I'm basically depriving myself of my main source of productivity and entertainment for an indefinite amount of time on the off-chance that it might solve a problem.
The solutions aren't really "cargo cult-sciency". :)
Originally, the solution was to keep an all white image to fix this as shown here:
http://en.wikipedia.org/wiki/Image_persistence
But, many have discovered that having an alternate black and white image fixes this faster.
Some swedish researchers managed to fix this by applying DC voltage to the lcd matrix and made some patent on this if I remember correctly.
The purpose of the method is based upon the theory that the electrical field in the matrix where you see the image persistance is disturbed by having the same polarity applied for a longer period of time. Perhaps causing a static charge or something influencing the ionic compound in the LCD.
When a screen is turned off for a longer period of time, the charge is diminishing and this can fix itself as said in the above link.
However, the lcd crystals move by applying current and having an alternate black and white gives max current for full off and full on.This is believed to stabelize the electrical field and thus removing the image persistence when applied to over time.
Usually the image peristance is most visible by viewing a mid grey color, so you might make one .bmp of that to monitor the progress? :)