If it's basswood, and not ash; that changes everything! However, it shouldn't be overly bright with high quality basswood.
Basswood is not noted for tight bottom end though.
I believe that a air Norton would actually be too fat in the neck position of a basswood guitar without a maple cap.
If it is basswood, then take note, that the Breed neck and bridge models were designed specifically for Vai's basswood Jems, while the Evo's are used on the alder body Jem screemers. Earlier on it was PAF Pros in most positions on most guitars.
A close cousin of the Tone Zone was used on the EBMM EVH basswood guitars, in conjunction with the Norton derivative neck, but these guitars had thick maple caps along with maple necks too. Those type of pickups may deliver a more later EVH type tone in a basswood guitar.
Satch uses PAF Pro derivatives in his guitars, many of which are basswood.