-normalize is a simple command that fails in your case.
It findes the highest and lowest values in the image, takes off 1% more, then scales all the channels so those values are the maximum/minimum for each channel.
It is rather brain dead.
The problem for you is that 1% Instead you will need to use
-contrast-stretch 0%, which works in exactly the same way but lets you specify the about of extra inward color to take off.
That will remove the extra 'burn' you see.
When I have finished work on image distortions I will be looking at the color methods developed by Fred Weinhaus in his IM scripts for auto-levels and other image enhancement. See
http://www.fmwconcepts.com/fmw/fmw.html
In the mean time you may like to use his scripts for your images.