The original photograph
I first used the Hue Saturtion and Lightness which made a better picture.
I played around with the Hue Map settings but didn't find any changes that made the photo any better, in my opinion. I did add an additional lightness shift, perhaps too much, but that was it.
Just to play around with the Hue Map, I changed the blues to purple. I think I'll leave this exercise for another day!