i certainly thank you for the effort involved in making that image. I was able to see a noticeable shift in saturation between the perceptual layer and the saturation layer, but only in the second horizontal bar in the magenta. Without using a spectrometer, I don't see any differences in that same bar in my prints from Photoshop and Photoline.
If the only difference you see in my tiff on your sRGB (I'm assuming it's full sRGB coverage) display is in just the magenta patches, I can't help you. I have looked at it on my lowly laptop display which has only about 70% sRGB coverage, and I can see differences almost everywhere, but it's just a lot harder to see them in the lighter, less colorful patches. Have you taken the X-rite color test
before? What is your score?
Your image on my sRGB monitor is more saturated than my prints to begin with.
Well, its a crop of Outbackphoto's ProPhoto RGB printer test image, not mine, rendered into one of my custom printer profiles.
The lighter and less colorful patches as well as the near-white and near-black parts of the gradients are definitely possible colors in many real world color images, and may be more useful for your judgement.
I don't think I know what is up with all this.
Certainly if your images comprise a tiny gamut, well within sRGB, then the differences between rendering intents will be small and difficult to see in side-by-side prints or side by side on a display. The flash-to-compare trick with layered renderings or using the preview function in Photoshop's soft proofing makes it a great deal easier to catch subtle differences. Then look out for those differences in your prints. It's a great way to train your eyes.