Yep, that's the charm of ATK, not like Stingray, not like P-Bass, something as a cross-over with its own growl-sound.
Perfect description on the ATK sound. The one bas stone it definitely doesn't do IMO is anything resembling a Jazz bass.
I always decribe the tones like this:
1. TRAD setting - Pbass-ish
2. BRIGHT setting - Modern/active P-bass-ish
3. ATK setting - Stingray/Sterling-ish
Notice the "ish" in every description - ATKs are their own thing.
J