I had a play with the jpeg you posted in the original post, so this is obviously a low res hack job - plus I used my iPad, so no photoshop here.
I first went to curves and eased down the red channel in the middle and shadows part of the curve, just to eliminate the orange from the sky. This has actually removed some of the milkiness- the smaller stars in the spiral arm - and if I was on my laptop I'd be brushing them back in. I then used a brush and painted over the Milky Way with saturation and details (clarity) enhahancements. I dodged the smaller galaxy slightly, but that hasn't been very successful on such a low res image. Finally I removed saturation from the bike, dodged the camp area and cloned out a couple of tiny distracting details.
I'm not saying it is any way near perfect, but it may be closer to what you hoped to capture:
