Both of my ceramic white and black PSP have dead pixels, but I have not replaced LCD screens yet.
However, I have taken apart PSP several times and replace power boards and buttons before. I have purchased parts from eBay and somehow boards looked slightly different, I was able to fix a few of my friends' dead PSPs. Opening wasn't too tough; just 9 screws in the back and about 13 screws inside. If LCD bought from eBay or some other place comes with the backlighting, I'm sure it isn't too hard since all you need to do would be unscrew 9 screws in the back and bottom and unhook the LCD, replace the LCD and plug tiny power cable and a ribbon cable. You just need to be careful with those ribbon cables because I had to buy one of the PCB boards again because I snapped the ribbon cable locking mechanism once.
I wonder if I can buy the better screen used on TA-086 PSPs on ebay...
Edit: I don't know about other people, but the dead pixel checker/remover homebrew software didn't do anything for both of my PSPs. I've tried two different video versions, a homebrew software version and none of them worked although I followed their readme/faq. In fact, I think one of the video version made it worse because now I can notice dead pixels on my black one even more.