Help with a scanning problem - surface reflections on a photo

I'm back at home for a bit, and I'm trying to help my parents scan an old photo when I'm here. I've never done all that much photo scanning, and I've found a problem that has me stumped. So I turn to you, the internet... (more specifically, my friends on the internet, but strangers and enemies are welcome to reply too)

Here's a flickr post with a portion of the scan, to get you started:
http://www.flickr.com/photos/cflake/155311298/

...and the real photo, if I can get it to work:


The photo doesn't have those white spots when you look it it normally, but when I use a 10x loupe and have the light at the correct angle, I see reflections as well. I haven't had much luck removing the "noise" with Photoshop (v7), so I'm looking for other ideas.

There's a small corner of my mind that thinks the reflections would go away if I turned the photo 90º and re-scanned, but the rest of me doubts that would work.

I could take a digital macro shot of the picture, but then I have to deal with shadows, any warping of the paper, and DPI conversions that I don't want to think about.

One forum post on the web said that wrapping the photo in good quality plastic wrap would eliminate some of the glare... but that was just one guy on some random forum.

The closest match that I've found on the net is this part of the FAQ in scantips.com:
http://www.scantips.com/faq2.html#moire

...which tells me: 1. I'm screwed, and 2. try the digital thing I mentioned before.

Has anyone else had to deal with this? Any good ideas?