Give it a try - it should work better, especially in the shadows. If it won't help, try to calibrate the panel at lower luminance.
Rel Col and Perceptual each have their place, depending on the image content. Just make sure to print with the same choice as you used in the softproof.
Also, are you adjusting the softproofed version of the image to resemble the unsoftproofed duplicate image as much as possible?
Another factor: What are you using as your print-viewing lighting? How the print appears in relation to the softproof is dependant on the color temperature of the viewing light, which should probably be 5000K. The intensity of that light should match that of your monitor, as well.
Also, after all is said and done, the detail in the shadows will be more apparent in the display, which is likely to have a greater contrast range than the print, regardless of the print-viewing light. Having the display luminance brighter than that of the print viewing luminance is also a problem.