You may try a wavelets decomposition. In a nutshell, replace the first two layers of the binned image (upsampled to the unbinned size) with the first two layers of the other image.
How to do that:
- Delete the first two layers on the binned image (previously upsampled and registered with the unbinned image).
- Clone the unbinned image, and delete the first two layers on the cloned image.
- Apply this PixelMath expression to the clone: "unbinned - clone + 0.5". Disable rescaling, and replace the image.
This will create a high pass image, where you have only the information of the first two layers. Now we have to add this data to the binned image.
- PixelMath: "binned + clone". Enable rescaling.
You may try also using a mask derived from the luminance, to target the high SNR zone more, and thus preventing too much noise to contaminate your background. I would use a blured luminance as mask, with the histogram adjusted.