I am confused by this remark.
The average difference between the colors requested by the graphics card and those displayed by the monitor, or the DeltaE, is only 3.2. Anything under 3 and only the very practiced eye can tell the difference. Setting the colors in sRGB rather than 6500K improves results even more and gives a deltaE of 2.8.
If a lower than 3 is bad how can a 2.8 be an improvement? So do you want to Set the colors in sRGB?
\