Photogamut works like an oversized printer profile ... this is why perceptual is available here (and actually works really well). Regarding it's original target (encompassing all printers) it's a bit dated (today some printers provide larger gamuts)... but as an intermediate color space to go to sRGB or similar purposes it's still very useful.
The left image was converted from ProPhoto RGB, relcol to sRGB.
As shown in post #2 there's a perceivable loss of image details.
The right image was converted from ProPhoto RGB, perceptual + bpc to PhotoGamut RGB.
Then, a Local Contrast Enhancement was applied through an inverted Saturation Mask.
Finally the file was converted relcol to sRGB as well.
For the purpose of showing it here, the screenshot was pasted in a new file, monitor profile was assigned and then converted to sRGB again.