This doesn't go directly to your original question, but IMO with general flourescent lighting you will always have difficulty copying artwork. Even though it's rated at 4200K it likely has spectrum peaks, often in the green, giving the effects you described, i.e. a tendency toward green tints and dirty reds/browns.
There are newer flourescent lights that purport to be more suitable for photographic work, but the nature of the technology is it always is going to have spectral "bumps", unlike incandescent lighting which behaves very much like sunlight, only at a lower color temperature. There are halogen bulbs at 4500-5000K, but I don't know of their suitability for copying use, i.e. do they put out enough light and they are very hot.
Richard Southworth