Is the V2 3 pickup version not closer to your sound?
Just a personal view but I see the Cat bass as a vehicle for the Nordstrand Cat pickups. If the V2 doesn’t do it, wouldn’t you be better looking for a short scale, lightweight Jazz bass, if that is the sound you are after? Fender Japan short scale, or spec up a Maruszczyk Elwood (they do a chambered version), or a Vox Starstream 2S (even Artist version if you can afford it).
That’s a good point, but I’d rather not spend a thousand dollars where I could probably get a solid sounding thunderbird pickup that fits in the Acinoynx

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