Don't know whether any of this would be affected by the fact you are running a dual-screen setup.
I have managed to get prints to come out satisfactory (to my eye) compared to what I'm seeing on screen. With some caveats.
Caveat 1. What I see depends on the ambient lighting. This is true for what I see on screen and what I see on paper. For viewing on screen, to get the most subtle renditions of gradients and details in shadows I need to dim the lighting in the room. On paper, for the images to seem really vibrant, I need to look at them in strong natural light. Even so, the images on paper (seen with reflected light) don't seem able to match the luminosity of images on screen (seen with transmitted light). That said, the highly luminous screen versions can sometimes look unnaturally bright/vibrant/punchy to me, and there can be something very appealing/special about looking at a well done printed image.
Caveat 2. Even with a calibrated screen, what I see on screen depends hugely on the precise vertical angle at which I view the screen. I use QuickGamma to keep the screen gamma at 2.2, but by raising my head an inch or so from the position where QuickGamma shows as 2.2, I can get the gamma to show as 2.1. The impact of this is easily seen when viewing images - as I raise my head from the optimum position the image "flattens" in its contrast and colours, and if I move far enough up the colours become "washed out". As I lower my head from the optimum position the image becomes "harsher". These are exactly the same effects as I get in Photoshop by changing the gamma of an image.
Caveat 3. The paper finish and reflections from printed images confuse the issues. I find glossy paper gives a more punchy image but glossy prints are very prone to reflections. I find these reflections so distracting that I go for the lower reflection "silk" finish prints despite the loss in impact.
Getting prints to look like the screen version. I use a commercial printer who uses two makes of printer. For the printer they use for images of the size I want (A4 and 16x12 to date), they provide a profile for use in Photoshop. I edit images in sRGB, and then for a printed version the final steps are (a) convert image to the exact pixel dimensions needed for the size of print on the specified printer, (b) print-specific sharpening, and (c) convert the image using the printer profile. (And on the print order, tick the box for "don't auto-adjust the images".) The paper versions produced this way seem consistently to match the screen versions pretty well.
For this to work you need a calibrated screen.
Calibrating the screen. Having tried several free, software + eyes calibration techniques, I settled on QuickGamma. To test that the calibration is ok (or at least as good as I can get it) I use things like the
Lagom Calibration Tests, Norman Koren's
Monitor Calibration and Gamma page (starting about half way down, at the Gamma and Black Level chart), Imaging Resource's
Monitor Calibration: Who needs it? page, and this
Web Browser Colour Management Tutorial. Because the results seem ok I have never got round to buying a device.