Dave,Your suspicion of whizzer involvement seems on target. The 'mechanical crossover' from main cone to whizzer is specified as 4500 Hz.
Have you tried placing some dacron between the whizzer and main cone? This often helps resolve whizzer-related peaks.
Some of the peaking could also be caused by edge resonance of the whizzer. A few coats of damar on the outer quarter to half inch of the whizzer might be all thats needed. Probably no need to coat the entire cone and whizzer. Avoid getting damar where the whizzer is joined to the cone - it hinders decoupling of the whizzer, causing a loss of HF.
Best Regards,
Bob