Okay, this is just a guess...
It looks to me like there's a double diffractive edge below the tweeter, formed by the horizontal slot on the front baffle. The ear might be picking up this diffraction as a secondary sound source with a seriously skewed spectrum, as it will occur within the critical .68 millisecond time window between the arrival of the first sound and the kicking-in of the precedence effect.
You might try stuffing something absorptive into that slot, like a thin slice of foam, or otherwise smoothing it over (maybe just a piece of masking tape would help - or better yet duct tape, for that macho look). While you're at it, tape a piece of foam or felt or something along the top edge above the tweeter as well. The sides of the cabinet look like they're nicely radiused, so I don't think they're an issue.
If this helps, you might consider going all the way and contacting Jim Goulding at diffracionbegone.com, as his felt tweeter surrounds work quite well (they received a Golden Ear Award from TAS a couple of months ago).
If this doesn't help, I have another idea but its implications are more expensive.
Duke
dealer/manufacturer