Thanks Gill! 
I don’t know that printer but the high-end Canons should be excellent with excellent paper profiles. There should be no need to fudge the monitor calibration. Setting up correctly should give the same tonalities in a print as in an online image. There is an issue with the darks in the online images, as shown by the histogram – which you recognize.
I got the histogram from your initial post of the image. I opened it in PS, with a very important first step. I have PS Color Settings set to notify me of any mismatch in the profile of an image I open. Of course the profile of the image was sRGB, as it should be, but in order to see the histogram correctly I had to check the box to convert it to my monitor color space, which is Adobe RGB. That is vital to seeing the correct histogram.
Years ago you would see advice for printing better blacks to push the histogram like this, using Levels. But that was way before good monitors and good printers.
I’m not sure exactly how you are doing the initial black and white point settings. Is that in LR/ACR? You have a lot of tonal overhead in either end of a raw file. I strive for some sort of bell curve shape, although it may be quite skewed but it without “toes” there will be no tonal transitions to slightly lighter tones. The black areas will have sharply-defined edges and no detail.
I am always watching the histogram as I do a raw conversion in LR. It is much more accurate than my monitor. But the center point is often skewed, depending on whether it is a dark or light image. It’s the ends that matter.