Not new strings?
Oh dear.
Do that, then see what its like.
New strings > all else.
Consider gauge as well. If the strings are very slack then high frequency overtones can get overwhelmed by the low frequency energy in a wide oscilation. You might want to tightnen it up somewhat.
Not all tunomatics are created equal. Whats on there now?
And theres a lot of leeway in a setup to affect the sound of a guitar. Flatter neck, lower action *tends* to brighten things up (it may not though; guitars are all different in this regard and I spend a lot of time tweaking action and relief in tiny increments to find the combinations that allow the guitar to resonate in the way most pleasing to me). Dont expect a night and day change though.
Nuts are a big deal, but remember that that only strongly affects the sound of open strings.
On that note, stainless steel frets are often reported as brighter sounding (and sometimes as making no difference).
Pickups being too close to strings can affect the strings resonance as well. If they're really close to the strings, like 2mm, back them off. Especially the neck.
But it may just be the guitar. If its mahogany through neck then they can be very dark (through neck promotes more dominant LF modes in the guitars resonance, and add to that the mahogany, plus the likelyhood that the mahogany isnt very good mahogany and you have a very dark guitar indeed),
The final thing I'd bear in mind is, that spalted top may just be killing the guitar, or exacerbating the problem. Its very pretty, but its an acoustic nightmare. All the little black lines are breaks in the woods grain caused by fungal infection of the wood, and the wood has basically no structural strength, its just mush, and mush is what it can do to a guitars sound. If the top is more than a veneer then it *might* be the problem (or adding to it).