I have the same configuration as the OP: Benq monitor (SW271) and Eizo (CS2420), and I use an i1 Display Pro.
First: update to ColorNavigator 7, and check you are using the latest Palette Master Elements, in case there's an issue there.
I too found a discrepancy in white point, but it was worse if I calibrated to a CCT, i.e. a temp like 6500K. The Eizo was visibly more blue, as you have found. Bear in mind that this isn't a precise definition, so different software makes could make different assumptions.
However, D65 (or D50), are precise definitions. I now calibrate to D65, and if I measure the result with Dispcal, there is still a slight discrepancy (slightly over 100K as measured), but it's barely perceptible if I display pure white on both screens side-by-side.
I've found this with another monitor compared to Eizo, and I suspect ColorNavigator, at least with the i1 Display Pro, is slightly on the blue side, but the difference is much smaller when using Dxx white point, as opposed to xxxxK