Nothing will help you with GDI. It seems indexed images are too backward a technology for Microsoft to care. All you can do is read and write indexed image files.
There are usually two step when quantizing colors in an image:
1) Find the best palette for the image (Color Quantization)
2) Map the source solors to the found palette (Color Mapping)
From what I understand, you already have the palette in the database, that means the hardest part has been done for you. All you need to do is map the 24 bit colors to the provided palette colors. If you don't have the starting palette, then you will have to compute it yourself using a quantisation algorithm: Octrees or Median Cut are the most well known. Median Cut gives better results but is slower and harder to implement and fine tune.
To map the colors, the simplest algorithm in your case is to calculate the distance from your source color to all the palette colors and pick the nearest.
float ColorDistanceSquared(Color c1, Color c2)
{
float deltaR = c2.R - c1.R;
float deltaG = c2.G - c1.G;
float deltaB = c2.B - c1.B;
return deltaR*deltaR + deltaG*deltaG + deltaB*deltaB;
}
You can also ponderate the channels so that blue has less weight, don't go too overboard with it, else it will give horrible results, specifically 30/59/11 won't work at all:
float ColorDistanceSquared(Color c1, Color c2)
{
float deltaR = (c2.R - c1.R) * 3;
float deltaG = (c2.G - c1.G) * 3;
float deltaB = (c2.B - c1.B) * 2;
return deltaR*deltaR + deltaG*deltaG + deltaB*deltaB;
}
Call that thing for all source and palette colors and find the Min. If you cache your results as you go in a map, this will be very fast.
Also, the source color will rarely fit a palette color enough to not create banding and plain areas and loss of details in your image. To avoid that, you can use dithering. The simplest algorithm and the one that gives the best results is Error Diffusion Dithering.
Once you mapped your colors, you will have to manually lock a Bitmap and write the indices in there as .Net won't let you write to an indexed image.