I think you are experiencing two things.
1. A reflected light print behaves differently than a backlit monitor, and
2. Very likely your monitor is two bright.
Here is a good article for you to read.
Since you ahve a profiler you can control things numerically; I would start with monitor brightness at 50%.
A lot depends on your work room conditions, but I would recommend no brighter than 120 cd/m^2 for your monitor. I work in a dim room, have no light shining directly on my monitor screen (monitor hood and light keyboard from above and slightly behind monitor), and have brightness at 80 cd/m^2.
Download the test image in the first article I linked to and then open it in your photo processing software. Do not make any adjustments to the image - don't worry how it looks on the monitor.
Print it using the appropriate settings; I let the program control printing, so I set the media type and ICC profile in software. You can do that in PSP.
Then, see how the print looks. I've done this with a number of folks in person and given this advice in the forum. Turns out the print looks great. If you're happy with the print then you need to turn down the monitor to match the print. In the off chance the print is too dark or bright then you can fine tune printer control and then adjust monitor.
In your print the trees look like they really are in shadow. Depending on the software you are using you might be able to brighten the shadows. You don't want a global adjustment since you would make other areas of the print too light.