I suppose if the three screen LED wavelengths were significantly different from the three camera filter wavelengths then you could:
Illuminate with screen Red to get Rscreen.
Illuminate with screen Green to get Gscreen.
Illuminate with screen Blue to get Bscreen.
Use ambient full-spectrum light to get Rfilter, Gfilter, and Bfilter.
Then you'd have 6 points on the spectrum.