Another wild idea:
Do you recall Sony's earlier Mavica cams? They had narrow lens on top to collect sunlight to use as backlight. I had one. Even in bright sunlight they are clearly visible, though a bit darker than perfect, never the less, pretty bright, brighter than backlight can do. Not transflective, regular RGB LCD.
See some Wikipedia's pictures. Clear line right above the LCD is backlight collecting lens.
So get one of those 3"-ers, reap back and fashion something Mavica style. Maybe Fresnel lens+mirror or lightguide + difuser (probably can use display's own).
(side thought - why they don't do Mavica backlight on other cameras now? Patent got to be expired by now!? It is way older than 12 years!)