How to remove a repeating 75 to the inch 'quarter-moon' pattern?

I am working with old images, including those from newspapers, and have become quite adept at repairing them with PS. I am familiar with most of the techniques for removing scratches, dust and half-tones, but I have difficulty in dealing with one particular feature of some of the photos unless I manually click about 50,000 times per photo. The feature is: photos that have been printed on a roughened surface that has a repeating 'quarter moon', 75 to the inch. A small sample can be found at:
http://jucreek.googlepages.com/temporary
When I am repairing a photo, I work first on a coarse scale on everything but the face; then I zoom in and on a much finer scale touch up the face, reasoning that people are much more aware of facial blemishes than elsewhere. In the past, with photos similar to the one in question, I take this approach one stage further: I try to remove most of the quarter-moon pattern (other than on the face) with the blur tool using a large diameter, staying away from edges so they are not disturbed; then I zoom in on the face, working on a much finer scale, and again staying away from edges and from the eyes. i.e. I leave the pattern on and around the eyes, reasoning that the eyes are the most important part of the face and unless the pattern is distracting when viewed normally, the eyes should be left alone.
Can anyone suggest a better technique for removing the effects of this quarter-moon pattern? It is of concern to me because at 75 to the inch I am pretty certain that the pattern is going to cause problems when I print the image. The original photo looks OK, but I suspect moire patterns will come to the fore if the pattern is not removed before I print.
Does anyone know what this pattern actually is? Out of approximately 2000 pre-1960 photos I have scanned, maybe only 6 or 8 have this type of pattern, and I think all of them they may have been studio photos.

I'm looking forward to the day (although I suppose I'll be long dead before it happens), when PS has enough intelligence to be able to remove spots and half-moon patterns by itself. When you can sit in front of your computer and say to PS:
i See all those spots, can you remove most of them the way we talked about yesterday. You know, make sure that after you remove a spot that us humans won't be able to detect the change. If you're not sure, how about flagging any spots you're not sure how to handle, and I'll go over them with you later on so you can learn how to do those yourself next time. I'm going for a cup of coffee. Shouldn't take you long, should it?
i About 3 to 4 minutes for that one. What'll I do after that if you're not back?"
i Put it on that page next to the woolscour, and make up a caption. You'll find the details in the photo file. And don't forget to add a gradient fade so the sky fades to nothing, and flow the text into the fade like you did for the swimming pool photo. I'll be back in about 10 minutes."
I can dream, can't I?

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