Here is one more theory I received from a marine biologist:
"looks like there are several candidates, if we limit this to
being a burrowing anemone, which I think it probably is:
Actinostola
Actinothoe
Ceriantheopsis
Cerianthus
It'd be nice if there was some scale. Judging from some of the
descriptions of these species, the pedal disk is probably deeply
embeded in the sand, and the mouth could be easily inverted and hidden
from obvious view. Could be more than one individual. Some of the
species above have oral diameters of up to 10-12 inches."
Hmmm... both the sponge and the anemone theories seem plausible to me. If I recall correctly, this specimen was at least the size of my palm if not bigger.