Stop, reset Color Settings to default and start from the beginning. You have set your monitor profile as working RGB, which is something you should never do! That sets color management policies to "off" and disables all display color management, thus defeating the whole purpose of using a calibrator in the first place. The monitor profile is ignored and not used with your settings.
Set working RGB to a standard color space, set color management policies to "preserve embedded profiles", and don't change that setting again. That's how color management is supposed to work.
The calibrator software sets the monitor profile up at system level automatically, no user action required. Just run the software and then don't do anything.
As for the screenshots, here's the correct procedure. You need to make the two screenshots separately, as per the following:
The numbers sent to screen have already been converted into the monitor profile. The original document color space no longer applies.
To get accurate color in a screenshot, you need to first assign the monitor profile, for the above reason. Then convert to a standard color space like sRGB.
For a dual screen setup, the two monitor profiles are obviously different. Photoshop color manages the two screens separately, sending different numbers to each screen for the same color.
Once you've made the two screenshots, assigned the corresponding monitor profile for each screen, and converted to sRGB, you can put the two sRGB files together and they will now be correct.
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