The following classic method is almost the same as you mentioned in your first post:

1. Duplicate layer,
2. remove transparency (Layer>Transparency>Remove Alpha Channel),
3. Filters>Blur>Pixalise, with maximum width and hight. (with your image 900*600)
4. Now you have the avarage color of the image.
5. Invert color of this layer (Colours>invert).
6. Set this color-inverted layer to Overlay (above the Original). Adjust opacity of this overlay.
....[you can also make an duplicate of the inverted layer and set it to Colour. Now you can combine different
....opacities from this two layers (Overlay and Colour)]
7. New layer from visible, duplicate this layer.
8. Possibly desaturate to taste.

After this: curves, color balance etc. etc. (now I didn't take this last step, so you can compare)

Your final take looks to be the most natural of all. Thank you so much for all of your tips, iarga. They are greatly appreciated!

Thank you. It's all about personal taste. I think I would combine the last one with the (more saturated) second. I prefer the colors of the second one, but appreciate the light values of the last. So I would layer those images and then try to get a nice result with blend modes. The most important thing is that you can try all these filters and methods and find a result you like.

Sometimes automatic color balance gives a nice result, but a lot of times you have to find a nice result yourself. Color casts differ from photo to photo. So you everytime have to search what's the best method to correct the colors.

I most of the times use curves first.

Very good tutorials by Pat David:

Basic Color Curves
Getting around in gimp color correction
Color curves matching

Sometimes it doesn't work with curves first, then I try methods I mentioned earlier. Afterwards I use curves and color balance etc. etc.

I would love if someone else has something to "teach" here about this subject. I also like to learn new methods and like to know about other (unknown) Open Source tools and filters to work with colors, color correction and color grading. I think it's fascinating.