I'm not sure its a problem with directivity or resonance based on the whole set of NRC measurements.
Consider a cleaner view of the on axis FR from the distortion graph:
View attachment 23502
It seems to me the tweeter is clearly tipping things up between 2kHz and 5kHz relative to the mid/woofer level. It also seems to me that off axis, those relative proportions are maintained pretty well.
View attachment 23503
Drop the tweeter level 4dB or so, and all you'd really see is that off axis dip around 4kHz, and the rise afterwards as a result of the tangerine phase plug.