One of the things Grissom harps on when he talks about his gear is that he dislikes bright, ice-pick sounds that make an audience cover their ears. He prefers a lot of bottom end in his sounds, and the reason there's a high-cut control on his DG30 Amp is to be able to reduce the treble even farther.
So it's entirely possible that, however much you like the look and feel of the guitar, it's not the right instrument for you, or at least, those aren't the right pickups for you.
My stock WL DGT sounds pretty darn bright to me with all of my amps, including the Marshall-Plexi-style HXDA. I have to turn down the treble with that one.
While mine has a Brazilian rosewood fretboard, ebony will be just as bright sounding if not more, so yours should sound pretty bright in comparison to most.
Which means...nothing. 'Bright' or 'dark' is an ear-of-the-beholder thing. It's all personal taste.
Since you're apparently using a profiler, is it not possible to put a virtual EQ item into the profile, use it to create a patch that boosts the highs a little, and use that patch with this guitar?
I don't know if you're a player who sits and plays through an amp, but sometimes when your ears are closer to the level of the speaker while sitting, it's shocking how awfully bright one's settings actually are.
That's one reason amps sound different miked up; the speakers are very directional in the higher frequencies, and you're hearing something different from when you're standing in a room; standing up, you're mostly hearing reflections instead of direct signal.
So if you haven't tried sitting with your ear closer to speaker level, i.e., closer to the floor, it might be worthwhile to see if that's a thing.
Also, a stage or studio with a hard floor and less furniture will often sound brighter than the room one practices in. Reflections from floor, walls, ceiling, absorption from furniture, etc, will affect what you hear in a room.
It is important, however, to remember that an artist-signature guitar will reflect that player's preferences and not yours. Ultimately the pickups might not be your thing.
Finally, try different strings. I don't know whether you're using the .011 ga. strings that come on the guitar; there are brighter or duller strings on the market you might try, and the gauge does matter.