Tried the following variations from the previous version.
(*) Added a dash of simple syrup.
(*) Instead of adding Sambuca, I rinsed the inside of the glass with absinthe
(*) Stirred the gulkhand after every ingredient was added (instead of shaking).
(*) Initially, I threw in some tonic water too.

The drink came out even better than last time. But still not perfect. I will go back to the Sambuca again.