The two things critical to getting the phase shift of the filter to zero are the source impedances feeding into it, and how well the two halves of the differential filter balance. Try opposite extremes of tolerance on the capacitors.
Yeah, well, not much I can do about the source impedance. The source impedance of the AC line coming is probably on the order of a couple of ohms. I don't think that would affect the current measurement much. The source impedance of the voltage measurement is high, though, because of the resistor divider.
How do you expect to see a fraction of a degree phase shift on those graphs?
How much does a fraction of a degree matter? pf = cos(phase_difference). So the maximum delta pf would be where the derivative (sin) is max, so pi/2, right? So, worst case error due to phase shift is when true phase is 45 degrees (and 135, 225, etc). So, say the phase angle is 45 degrees, but I measure 2 degrees off. That would get a pf of 0.731 where the true pf is 0.707, or 3.5% error. Not great, for sure, but something I'll have to think about tolerating given the calibration resources I have available to me.
EDIT: Whoops, that's not right. That's the point of worst case error in pf, not the point of worst case relative error. The worse case relative, I guess, would occur at 90 degrees, where the true pf is 0 and a two degree error would yield a calculated pf of 0.035. Relative to 0, that's an infinity percent error. :-) Like if I had a 1kVAR load on there, I'd be saying there was 35W of real power, when in fact there should be none.
I'll look into the caps being at opposite ends of their tolerance bands as you suggest. In general, I took 5 minutes to make that sim, and it needs more thought.