Hi Henry
my Hawk had identical problem and it was the bump map.
(i know it's stops when specular was removed) but bump was the problem.
something to do with the way they interact
open you bump map in photoshop
red channel copy to alpha channel first & name
Alpha 1 (notice space!)
then make 100% sure that
Red channel is Black
Green channel is Grey
Blue channel is White
I found that my Bump maps as standard had the red channel as Grey same as the green channel.
if you using Crazybump thats why as it once worked fine for FSX but since Crazybump 8.5 beta it has messed up my bump maps
but if i manually tweak the bumps in photoshop they work fine and strange specular shading dissapears.
Regards
Rick