I'm so grateful for the people who mentioned Fitswork! This is not my second attempt, just my very first trial with Fitswork:
No more than two adjustments in Fitswork and one in Photoshop produced this result.
Fitswork: adjust histogram, adjust colour contrast
In the screenshot below you can see how Fitswork opened the image (the mostly hidden window to the left) and how I increased the contrast with the histogram panel (left=0.01, right=0.32, gamma=1.39).
The nebula was still mostly cyan. I tried to increase the colour contrast with an adjustment in Lab colour mode. With the saturation at 131 the red was a bit more prominent. The cyan was now a greenish cyan (see the image above) and I thought I saw some colour gradient in it. I took a screenshot.
Photoshop: channel mixer
I opened the screenshot In photoshop. A channel mixer adjustment layer separated the colours in the nebula rather successfully. I set the channels at first to:
Red = +130 red, -15 green, -15 blue
Green = -15 red, +130 green, -15 blue
Blue = -15 red, -15 green, +130 blue
This just intensifies the colours. The problem now looked like 'too much green' rather than 'too much cyan', so I tweaked the setting for Green to:
Green = +60 red, +105 green, -48 blue
This oddly worked, as you can see in the screen shot.
The nebula looked much better after this, but the rest looked awful. So I made the mask of the channel mixer adjustment layer black and put a white dot on it, right on top of the nebula, so that only the nebula showed the effect of the channel mixing. I finally reduced the fill of the channel mixer layer to 75%.
What I want to improve:
The red of the nebula should be a bit brighter and more saturated. That might also add a bit of a yellow zone between the red and the green. A bit more red and less blue will probably do that. Like so:
Red = +145 red, -15 green, -30 blue
I think I can keep the blue as it is. The channel mixer is a bit of a magical mystical tool.
GIMP has one too, so the whole process here can be done with freeware.
Screenshot of photoshop working on the screenshot of Fitswork:
--- Click to see it full size ---