That's quite attractive! TY for sharing the link. There are definitely tons of store-bought cultivars I've never heard of. Next spring I want to buy more even though those are all either P. grandiflora or umbraticola. I'd like to find some of the other species, but looks quite unlikely in AL.
According to USDA plant database, P. amilis isn't even listed as being present in AL, but does mention Sesuvium portulacastrum, a similar plant. Hope I do notice/recognize it if I see it.
...I guess if folks knew the others well, where to get them, they wouldn't be rare!