Thanks Kevin for your Herculean effort. When making a final set of pictures for this, I'll take graycard shots for each surface. Here, I am most interested in the shapes, for example the forced curve in the seam of the rug and the light fixture which I like.
If it were me, I'd ask the custodian if he or she could temporarily turn off the pot lights. Then, I would have just the flourescents turned on. You only have one color cast. Or one general cast. I suspect that the ages and brands will affect the color casts.
Then, I'd see if I could work with just the pot lights turned on.
And, last, I work with everything on. You might find your lighting conditions better using one general source of lighting. It's when you mix and match that you have lots of troubles.
If you're mixing and matching light sources, I am not sure gray cards will help much. Yes, will you know the true colors of various objects, but it will be challenging to get everything working harmoniously together.
If you have one light source, then you can correct for its cast. If you have two diffrent photos using two separate light sources, you might find that you can blend the two color corrected photographs for maximum effect.
Anyway, this stuff is beyond me. Intuitively and not knowing more or better, this is how I would approach your indoor shot.