I haven't used Adobe Swatch Exchange, but I work with theme files and color libraries a lot, and the way I personally like to organize my swatches is actually very close to what you have mentioned:
- Primary color + primary derivatives (shades);
- Secondary colors + derivatives;
- Complementary colors that are part of the palette;
- Special case colors (because I work with apps, a special color can be the alert red, for example);
- A gazillion shades of grey with different transparencies;
- "Everything else".
It really depends on how many colors you have and how you use them (maybe a sample image would shed light on this!). You could potentially add ones you are not currently using but belong to the 'allowed' colors the designer can use.
The way you do it is more or less flexible, but the grouping and hierarchy should be fairly clear, so I'd definitely try to:
- Separate and distinguish the primary/secondary colors
- Group shades / tones of the same color together