Well...
If the the profile was properly created and the softproof looks similar to the print but both are quite different from the original image, most likely your image have colors that are out of gamut for that printer/paper combination.
If that is the case, nothing you do will make it print those colors. You may try another printer/paper combination (if available) with larger gamut or adjust the image until you get an acceptable appearance, but knowing that you will never reach the original colors with this printer/paper combination.