I have no idea if you could be successful in this, but if I were going to try it, I'd use the frosty side of aluminum foil smoothed down really evenly as the "mirror". Or maybe some aluminum paint sprayed onto paper (or even onto the backlight spreader itself if you don't care about the backlight anymore) Obviously you need to be careful with metallic mirror surfaces to avoid shorting out electronics though.
I haven't seen inside of any backlit portables, but there's a good chance that the backlight is sandwiched between the LCD and a PCB, with finicky conductive rubber connectors between the screen and the board. If that's the case, trying this carries a high likelihood of putting very annoying lines of "dead" pixels in the screen, where the finicky rubber contacts failed to seat as nicely a second time as they did the first time.
Patient and careful dissection and analysis of the device would be the way to go, stopping if it looks like something might not go back together nicely if dismantled.
If I had one of these, I might look into it myself, but I don't. I have a laptop that I wouldn't mind being transformed into a reflective screen, but it's a bit expensive for the experiment.... =/