Using only 5 colors in image mosaic...can't index

I want to create a "pushpin portrait" but only using the 5 colors of black,white,red,yellow and blue AND instead of having the pixels square, I need them to be circles instead...like a mosaic.

Here's a test I did.  First I created the rhinestone shape (rough shaped), with transparent background). I used a size of 30px and made a pattern of it.
Then I took this photo and reduced it to the number of pixels that I wanted for each of the dots.  So in this case, I wanted 100 dots across the top, So I reduced the image to 100px wide.
Then I converted it to index color with the five colors your wanted: white, black, red, yellow, and blue.
After that, I converted back to RGB and upscaled it using nearest neighbor to keep the pixelated look.  I upscaled it so each pixel was my pattern size of 30px, so 3000%.
Then I created a blank layer under this pixelated layer, and used the fill command using the pattern I created in the first image.  I clipped the pixelated layer to the fill layer, so that the colors would just show where my pattern had pixel values (round dots).  Then I set the pixelated layer's bend mode to overlay to get the look of a rounded dot.
It looks a bit flat, but you can play with different patterns to get different looks.  I also put a solid black layer under everything to fill in the gaps between the dots.

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