Sorry I wasn't being clear -- the RGB camera response to each patch of a swatch should give (up to) 3 different constraints under normal lighting, plus another

Sorry I wasn't being clear -- the RGB camera response to each patch of a swatch should give (up to) 3 different constraints under normal lighting, plus another 3 by cycling through LED colors, so in theory you only need ceil((k+3) / 6) colors to estimate a k-variable camera response curve (the other 3 estimate your LED wavelengths).