@OP:
I know that your stated concern was the differential photobleaching in the print. However, there is another very serious (but easily fixed) problem with the images that you posted that make it almost pointless to work on these scans. This is because while it might be possible to get the dark band around the edge to look like the adjacent interior areas, the brightest details in the interior region are now forever lost in your scans.
You seriously overexposed the scan. My guess is that you either (a) had the scanner set on the wrong mode, or (b), you manually set the scan parameters incorrectly, or (c) the scanner's "auto" exposure mode is not very good.
Specifically, when you are trying to retrieve highlight detail from a print or other document that is already quite light, one of the worst things one can possibly do is to overexpose the scan. Doing so essentially guarantees that no one will be able to extract good tonal and color information out of the bright areas on the print. The very brightest areas in your print should map to no more than 245 or so after the scan. Currently, even areas in the print that are not all that bright are maxed out at 255.
The attached image clearly shows this. It shows your image thresholded at a brightness of 249 (out of a maximum of 255). Everything in the scan brighter than 249 is shown in white. Everything under this brightness is shown in black. Notice how much white there is. There should be none or almost none.
I would suggest that you set your scanner on manual exposure mode and adjust the black and white endpoints appropriately.
A second way to improve the ability of others to work on your image is to save the scan as a 16 bit per channel TIF instead of as an 8 bit per channel JPG. Doing so immediately provides two benefits: 256 times finer tonal resolution, and no JPG compression artifacts (clearly visible as the blocks in post #2 in this thread).
If you can provide a better scan, it will provide our members with a much better starting point, as well as more motivation to work on your request.
HTH,
Tom M