Seems youre all barking up the wrong tree. The OPs "light tent" is badly designed. Structural design is OK but his built in illumination scheme is verrrrrry wrong. His lighting scheme is backlighting with bounce for fill.
That scheme is routine for Vogue fashion cover shoots, where low contrast smooths skin texture, mutes color, and softens facial detail. He is getting pretty much that same effect on his coins according to his description of his results.
All the petty hand wringing about CRI and calibrating monitors is chipmunk chatter. The color is a matter for PP. The ENTIRE problem is the lighting. Theres no actual color problem. Coins are obviously not colorful, so CRI is meaningless. Whichever color coins are, silver, gold, or bronze, theyre monochromatic. Dial in final color in PP.
The OPs lighting is all wrong. He needs more toward the front of the tent just outside the FoV.
The backlighting needs to be very greatly reduced relative to the forward sources. The forward souces should not be a complete surround, IOW not all four sides. Main lighting from left and right, with less light from above, would give good modeling of the coins. Or have no light at all from above but dont have a white floor below (black or grey).