Hi Doug - I have followed your instructions. Not sure why I could not upload here, not Jpeg? Too large?
I hope this link works!
https://www.dropbox.com/sh/lkffz2nglpv1jx8/AABDij-BFr00SQsv_LmVo9coa?dl=0
Exactly what I needed. Thanks.
A few comments:
It's clear the big problem is on the printer side but not related to the profiles. Neither profile should result in the dark blue shift you are seeing on your prints. I would install Photoshop on a different machine and print the image there to see if there is some sort of driver issue. If possible use a Windows machine.
That said, there are lesser issues with the profiles. The custom profile exhibits some unusual non-linearity in the Cyan regions. I'm going to look closer at those. Also, the custom profile is a V4 profile while the canned profile is V2. That shouldn't affect Relative Colorimetric printing but you will get more consistent results when using Perceptual if you generate V2 profiles from the ColorMunki s/w. However, none of this explains the strong blue shift you are getting.
On the positive side the black point is around L=19 on both profiles with maybe a deltaE of 1 difference. This indicates the canned profile is not, incorrectly, incorporating a BPC inside the profile for RC. Some OEM profiles do this.
Also, the image itself exhibits a strong "S-curve" characteristic of output referred image capture. One side effect of this is that lower luminance are reduced further and high luminance regions are compressed. This is also evident in the capture with a colorchecker passport that was posted earlier.
More later.
I grabbed a cyan section from the right side of the ProPhoto image then ran a round-trip using Relative Colorimetric for the Custom and Canned profiles. These colors are roughly around the printer's gamut boundary. The attached image contains the histograms of the resulting deltas and the image section from the original in ProPhoto. Horizontal axis are the deltas.
The canned histogram exhibits typical behavior near a gamut boundary. I suspect the Custom, ColorMunki histogram looks like it does as a result of too few patches to create good profile LUTs.
However, this is a curiosity as the effects are still very small compared to the strong dark blue shift William is getting. The printer issue clearly needs to be resolved.