Sorting (CIE)LCh colors

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I have a palette of RGB colors (RGB555 "color space", image 1) which I converted to (CIE-)LCh. I want to present that palette in a 2D image so the user can pick colors from it. The colors should be "close together" (perceived color distance). I thought sorting colors by H,C and L and by H and L*C (image 2) should work somehow, but everything I tried looks rather random. I am pretty sure my color conversions are ok. How can I sort the colors in a "pleasing" way?
RGB colors enter image description here

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