Well, you want to drill through the plastic and if it slightly goes into the stone bottom that would be good. On one of my drums I purposefully went into the stone a bit and put little metal pieces before epoxying. I found this is unnecessary because on the other 4 I fixed, they didn't need this extra precaution.
Like Rene said, make sure the epoxy label says it is suitable for plastic. At my local hardware store most of them were.