If one aims at reproducing the Color Checker Proof Chart that way, the choice of one of the Colormetric renderings should be the first decision in my opinion. The profiles describe the gamuts of the individual devices, the rendering choices how each gamut/color space is translated in the other one. With that the dynamic range. The last must be wider in the paper print.
That the shadows-blacks are not separated enough with the Perceptual rendering despite a deeper black in the print could have two causes: first, your viewing light is not giving enough light for your eyes to make that separation and second, Perceptual rendering is still a manufacturer's solution. That extra light will make the divide between the print and the chart even wider though. The OBA content of the Fine Art Baryta is probably higher than what is in the chart base so any viewing light with UV content will throw in another spoke.
If you want to compare results with other sources:
Babelcolor has some information on the chart's colors, averages and deviations (whites too), and a variety of CC image files in different color spaces:
http://www.babelcolor.com/main_level/ColorChecker.htm#ColorChecker_charts_imagesHahnemühle must have the media preset + profiles for that paper and the Z3100.
There's no mention of the OS you use which could also be important when you do not use the HP Z integrated profile creation system but make profiles through another path.
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Met vriendelijke groet, Ernst
http://www.pigment-print.com/spectralplots/spectrumviz_1.htmJuly 2013, 500+ inkjet media white spectral plots.