Never mind all that. As they say, you're barking up the wrong tree.
What you want is the native setting. Those other settings, sRGB, Adobe RGB and so on are all emulations, restricting the monitor's gamut in one way or another (yes, even Adobe RGB). You don't want that.
If you don't get a match, your calibration targets are wrong (or you're using the wrong printer/paper profile). Set your targets so that you have a visual match between monitor white and paper white. Then set a reasonable contrast ratio (black level) that matches the paper. Very few paper/ink combinations exceed 300:1.
Or, of course, your "non-matching" colors are simply out of gamut (either display or printer) - meaning one can reproduce it and the other can't.