What to do about moldy marble shower shelves?

In our walk-in shower that were part of a master bath reno 10 years ago, we had installed three corner shower shelves made of marble. I'm regretting that decision, as cleaning them over the years has proven difficult... they're now stained and pocked and attract mold and mildew under anything that sits on them. Gross! I had wondered about using a cement countertop product that I've seen folks use in kitchens to re-cycle them. Good idea or bad? Any other ideas out there? The rest of the shower (tile) is in great condition.

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