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Blutaparon vermiculare
On some high ground at Fort Island Gulf Beach
Good point, I had the right family but was off a bit. This new suggestion should be it, I am quite sure.
Similar, but the leaves are not as succulent looking as the plant in my photo. Though it does say it is near coastal areas, so maybe we are getting closer.
The flowers don't seem right for the pictures I could find of Sesuvium portulacastrum.