How is an ICC profile embedded or built into an image?
I realized that littlecms, suggested by joojaa in a comment above is very complete in dealing with the ICC profiles.

I did a few tests in their color translator program with different destination color spaces and the differences are great as you can see:

Original



sRGB-like



adobeRGB1998 (it seems it's the original color space)



appleRGB



And the most desirable results in my case are within the ProPhotoRGB color space:



linearProPhotoRGB



All of the above were following an automatic rendering intent but other intents bring slight variations (samples applied together with linearProPhotoRGB destination color space):

Absolute Colorimetric



Legacy Unadapted Absolute Colorimetric



I also realized that GIMP was actually restoring the original profile (not the opposite as I thought, i.e. instead of applying an embedded ICC profile, it was taking it off) and with this littlecms, now it does seem much simpler to "translate" color spaces than I thought.