I can't recall Fender having made exactly what you're after.

The Mike Dirnt Precision Bass is probably the closest, but it doesn't have the J pickup.

The Big Block Precision Bass is another option to check out.

And the rank outside option is the Frank Bello Signature Bass.

All are current production offerings.

Btw, the Sting has the mid-50's-style body with the contours.

Aide toi et le ciel taidera (Aid thyself and heaven will aid thee)