After you mark the center of the base of each cylinder, you could build a wood clamp to hold the cast part while you drill it with the press drill.

That clamp will fit over the round regular surface.
A piece of leather will protect the part from scratch (or from accidental rotation when the wall of the cast part becomes thinner and thinner).

To align the hole with the part, a hollow support (like a metal can) over the table will help.
Since the material is soft, you may be able to hold the wood clamp with your hand while you drill bigger diameters in small steps.