I think it's the wrong kind of bass to try for an acoustic bass sound. Everything on an Alembic fosters sustain - through-body design, laminate neck, heavy hardware. The predominant sound of an upright bass is very short sustain (certainly when you're playing pizz). When you pluck a note, it gives a big transient, then dies down very quickly. That's what makes the thump. With a Series bass, you'll have a much more gradual decay of the sound, much less decay than even a traditional bolt-on bass.
If you really want to try this, then I would think about putting a big piece of dense felt or foam under the strings right next to the bridge to kill the sustain off.
David Fung