Neckdive is mostly about the fulcrum point of the body, the upper strap pin. Beendown, your bass is neck heavy because that body was originally designed as a medium scale 4-string. Even as a medium scale 4-string the balance isn't anywhere near 1:30 or 2:00, more like a 2:30. So yeah, you add a couple of inches of scale length, and a bigger peghead with an extra tuner waaaaaay far away from the fulcrum point, and yeah, you got a real diver there. In fact, I would not take an order today for the bass you have. A
Making the body heavy is a terrible way to try and correct a bass that doesn't balance the way you want it to. The best remedy is to remove weight on the peghead. Use lighter weight tuners to start with. The other option is to extend where the upper strap pin attaches.
Sustain is great with all the woods we use in the neck. The super power of Ebony is fundamental sustain. Most sustain is the second harmonic otherwise.