Exposing that rock to high heat (90F and up) by pulling it out and setting a heater (or leaving a tub in the sun for a few days) will kill the plants that you see. It should greatly decrease reoccurences of Acetabularia, possibly also Neomeris.
You may be interested to know that Acetabularia is considered by some aquarists to be one of the most beautiful of the marine algaes.. it is typically cyclical in nature, with new crops of algae constantly growing and the blooms (discs) that you see lasting about three weeks or so.
>Sarah