Yes, this anemone have a lot of what you and Gary called eggs. I am still not sure if they are indeed eggs. I hope they are but when I first got her there was none but there are a lot of these shadow clusters on the column now.
Check out the paper "Gametogenic and reproductive cycles of the sea anemone, Entacmaea quadricolor" by Dr. Scott (I am pretty sure you have this because I have posted copies several times). Granted, the photos aren't of S. gigantea, but I have seen the same thing in E. quadricolor.
The sex of E. quadricolor individuals could generally be
determined by examination of the mesenteries prior to
histological sectioning. Female anemones were usually
distinguishable from male and non-reproductive anemones
by the presence of prominent green oocytes. During
the early stages of development, the oocytes were visible
through a thick layer of endodermal tissue that contained
highly concentrated brown speckled zooxanthellae in
the region above the maturing gametes (Fig. 4a). As
development proceeded, the oocytes increased in size
and became more prominent (Fig. 4b, c). The mesenteries
of recently spawned anemones appeared to have
empty sacs where the oocytes were previously located
(Fig. 4d).