OK, I think this is becoming quite clear. According to what I see from ColorThink Pro (CTP) you have produced an unprintable photograph. Please see the accompanying screen grab of the CTP analysis. The original pixel size of your photo weighs-in at 166 million. For CTP to work with this, I had to reduce it to 8 bit, then resample it down to 10 x 6.6 inches at 240 PPI using BiCubic Sharper, giving me a revised image size of 16M. That worked fine, the two versions look the same (see accompanying illustration) and CTP can handle this much image data. So I could open the reduced one in CTP. All the gorgeous colors you see there is CTP's extraction and reproduction of every pixel in your photo. Mapped against that are two profiles' gamut volumes and shapes: one for breathing color metallic (the gray blob) and the other for Ilford Gold Fibre Silk (the wire frame) which has an even larger gamut than Epson Premium Luster. You can see from this illustration, that most of the colours in your photo are so far out of the gamut of ANY paper profile that the colour management system would have a hard time dealing with this, and therefore hue shifts have occurred. You could try playing between Relative and Perceptual Rendering Intent, but not at all clear it would make that much difference.
You need to perform less radical editing, doing it under softproof, to see as you go in real time what the printer/paper combination can handle; see whether approaching it that way produces both a good photo and correct colour for you.