It's more likely to be related to frequency response than tweeter material. Axioms are very flat in the upper midrange while many speakers dip down several dB for a smoother sound. This is where the claim that "Axioms are bright" comes from.
A good first test might be to turn the volume down perhaps 4 dB from what you are used to and see if that makes a difference. If so, it is likely that you are sensitive to that "few khz" frequency range and might have to either EQ down or go for a less flat speaker.
There are claims from one guy in New Mexico that the titanium tweeters ring at specific frequencies, but (a) that would normally show up as both a coincident frequency response spike and distortion spike (which I don't see in the graphs), and (b) his motives are a bit suspect since he sells a competing brand and slimes pretty much every competitor in some way or another
