Lighting is very important when photographing coins. Too much and you end up overexposed which washes out details. Too little and you end up underexposed which doesn't give you details (the famous dark circle). This is why I highly recommend a non-reflective black or dark gray background. NGC slabs with their white inserts cause problems. You want the light that your camera collects to be as much from the coin as possible. The NGC white insert tends to cause underexposure; you get too much light from the insert and not enough from the coin. This is why I suggest using a non-reflective black mask to cover and much of the insert as possible with out blocking out part of the coin or putting a shadow on it. The ultimate goal is to have the picture look like the coin. Here are pairs of pictures of the same NGC-slabbed coin with and without a mask. These pictures show a slight but visible difference in exposure.
It's kind of like photoging a subject in front of a sunlit window......I 'stop down' the exposure a bit and do some correcting in post editing.
I've found that if the coin is underexposed or underexposed, due to the background or some other reason, you can use the processing software to bring it back to a true representation. I've been using Photoshop Elements for a number of years, but I understand there are better ones out there, some of them free.
I've got Photoshop Elements too but hesitate to use it to "improve" my coin images. I've done it in the past, trying to make a coin look really good. But when I compare the result to the coin I mostly find that they don't look the same. Or worse yet I can't get the coin look real in the images.
Your putting blockers and masks on Lady Liberty? You're taking this coronavirus thing a little far, kanga! Haha, just kidding. Seriously though, I hadn't ever considered the reflectiveness or brightness of the slab itself in lighting and composing a picture. I'm going to experiment with it a bit and see how it works for me - since the vast majority of my collection is NGC slabbed. I've been working with some DPLs recently, which have been presenting a particular challenge in the "black circle" department.
Yeh, proofs and DMPL's are a real pain to photograph. I think Goodman's book suggests axial lighting. I cobbled up an axial lighting setup but it was so long ago (~20 years) that: -- I don't remember why I did it, and -- I don't remember how it turned out. I don't collect proofs (except for my birth year set) and I don't have any DMPL's. Maybe it was just curiosity.