Cannot overcompensate a soft proof copy when 'Simulate paper & ink' check box is selected

The "haze" you get when you turn on Simulate Paper & Ink is just color management telling the truth: The paper has a much narrower contrast range than your display. The software for my calibrated display tells me it's 649:1. But the contrast ratio of most paper is something like 200–250:1. That's why you see a significant drop in contrast (that haze) when you tell soft-proofing to simulate the dynamic range that the paper and ink are actually capable of. I do have a different calibration for my display that uses a 250:1 contrast ratio for print editing.

When soft proofing is off, you're seeing the image shown as well as your calibrated display can possibly show it. When you turn on soft proofing and Simulate Paper & Ink, now the preview must be limited to the capabilities of the paper and ink. The amount of "haze" (contrast loss) depends on which paper and ink you're using. Generally, cheap and matte papers have a smaller gamut and lower contrast; expensive and glossy papers tend to have a larger gamut and higher contrast. This shows up in soft proofing. If you were to print on expensive glossy paper and select that profile for soft proofing, it will probably look much closer to the idealized view when soft proofing is off. You can see the variations in contrast for different types of paper in the animation below.

Canvas is typically coated for matte inks, and in combination with the canvas surface, it's just not going to look as good as a high quality glossy print or the display. And soft proofing shows that. The canvas profile I used in the animation shows that too. When you asked how you could get the soft proof to look as good as the master…you won't. Because the inks on that canvas cannot match the display, and that's what soft proofing is showing you.

The point of soft proofing is not to exactly match the on-screen master, but to get the best print possible within the limits of the paper & ink you are using, and canvas is relatively limited in contrast and saturation even when compared to other paper/ink combinations. You can't make the canvas and ink create deeper blacks and more saturated colors than it's capable of. If you want the soft proof to look more like the master, you must use a paper/canvas with more contrast.

But the reassuring thing is, the canvas print is probably going to look just fine. We see images on comparable media all the time and think they look great. As long as you don't put it next to the same image as a glossy print or computer display! 🙂

The print will never eactly match the image you see on screen - two different things entirely. One is reflective light the other transmissive. That being said, if you select a paper in the paper choices for your printer, and you select the matching profile for the type of paper you are using in the settings and make sure you do not  "double profile" meaning you turn off the color matching in the printer and let photoshop or Lightroom control the color, you should get pretty close to what you see on screen. The best profiles to use are those created on your printer with your ink and your paper. You can purchase the tools needed to create print profiles from XRite and they work very well, even if it is time consuming. You can get a specific profile made for you for about $99 and that is worth it if you print consistently on one type of paper and print a lot. Eric Joseph, of freestylephotobiz.com, can make profiles for you. You can also use the "canned" profiles that many paper manufacturers offer as a free download on their websites. RedRiver is one such company. If you are using one of their papers, and use the profile they created for that paper and your brand and model of printer, you will get excellent prints. I still use the softproofing to give me an idea of what might get dull in my print, however, with a printer and paper profile set, the prints get so close to the calibrated monitor image.

This video may help:

Soft proofing in Adobe Photoshop CC

In this 33 minute video, I'll cover soft proofing in Adobe Photoshop CC:
What is sof proofing.
Setting up a soft proof.
Saving soft proof presets.
What the simluate ink and paper check boxes do, why to use them.
Making output specific edits in layer sets.
Working with soft proofing in full screen mode.
The Out of Gamut Overlay and why to ignore it.

High resolution: http://digitaldog.net/files/SoftProofingInPhotoshopCC.mp4
Low resolution (YouTube): https://www.youtube.com/watch?v=njFgYba3lHU&feature=youtu.be

Edit: additionally 

http://digitaldog.net/files/LR4_softproof.mov

http://digitaldog.net/files/LR4_softproof2.mov

This probably isn't really a good answer. However, it is what I have grown to accept. A print cannot ever "match" the master image as you see it on the monitor. The monitor image will always be brighter, regardless of how carefully you have profiled the monitor. At least that is my experience. I use the soft proof feature in Lightroom to "approximate" the results as best I can. I have been using the same printer now for about four years, and can pretty well anticipate how it will respond. The soft proof helps in determining problem areas that I can correct, but I have learned not to fully rely on it for an exact rendering of how the final print will look. The picture will always appear brighter on the screen because it is backlit, and there are other nuances that will sort of "trick" the eyes. But I have learned to use the soft proof feature to at least anticipate where problems might occur to the point that my prints almost always come out satisfactorily. That's my take on soft proofing, at least the way I have been able to use it on my computer. If you want "perfect" Results and a perfect match keep working on it and watch for better suggestions.