I have done DSTN to TFT replacements but it is not easy. You'll need a CPLD (or small FPGA) with an SRAM to sample the exisiting display data (likely a 4 bit or 8 bit parallel bus with clock, hsync and vsync signals) and then convert this to signals that can drive a regular TFT screen. Sometimes the display data is PWM modulated to achieve various pixel intensities which means you need to capture several frames (2, 4, 8...) to make 1 TFT output frame. You'll only need 3 bit for the colors towards the TFT screen though. It all starts with capturing a few frames worth of display data and analyse the contents.
I'd look into how the backlight is working first and if that isn't fixable or OK, I'd look for a direct replacement of the display. Maybe you can find a cheap one that is better.