Amazing what people figure out!
Along those lines, you'd have to refine this as I just made it up. See if this effect would be in the ballpark of acceptable.
Dupe the layer, convert to smart object for further explorations and refinement of blur radius (I happened upon 1.9 for this), blur, invert, mask, reduce opacity to 50%.
The basic logic is as follows: by blurring the area you turn the moire into luminosity blobs that upon inverting counter those present. You might do similar with luminosity masking and curves, I suppose.
Anyway, I spent more time writing this up than I did playing with the technique, so give it a whirl and see if you can refine it.