...Aaand I'm quoting myself again to show how I solved the issue.
After having the neck diagnosed, under Sadowsky's CS suggestion, by a very well regarded local luthier, who basically told that the thing was structurally perfect and just had a tiny dead spot, I just accepted the fact that this was a case of "acute bad luck", so to say.
Having verified the impact that adding mass to the headstock has on the sustain of certain notes, I just bought a Fat Finger that, once correctly placed, has made the dead spot virtually nonexistent. Not that aesthetically displeasing either.
I'm a bit anxious to see if the thing will stay put after some extensive out-of-home use, with the bass being carried in a gigbag. Also, we'll see if it will react in some nasty way with the nitro finish of the headstock.
All in all it could have been worse though, I'm loving this bass, it's just solid. It works. And it's so versatile. Its capability of slotting itself in almost any mix reminds me of P basses in a strange way, although the two have very little in common. Those flats may have something to do with it, as well