FFT really doesn't help here sadly, we get many textured prints at work to use as a source (which is very annoying, if you are planning to have some packaging made and are planning to send a textured print to become the main image, don't! - rant over).
We use one of two methods:
1. The low pass method;
Duplicate the background layer, use Filter>Noise>Dust & Scratches with a threshold of 0 and the lowest pixel level that removes the problem.
Then set that layer to Darken blend mode.
It does lose fine detail.
2. Double scanning;
The reason you get these highlights is because the light source in flatbed scanners is not at 90 degrees. Luckily though, they are rarely at 45 degrees either, so...
Scan the image then rotate it 180 degrees on the scanner bed and scan it again.
Place both scans on different layers, rotate the upside down one to be the right way up.
Carefully align the scans (Later versions of Photoshop have an auto align layers function in the Edit menu which is great)
Set the top most layer to Darken blend mode.
Better detail retention.
Takes twice as long.