Well let me just say that I am jealous, you have your own tropical getaway in your own back yard! I know a lot of people in california grow the ice plant. My mom is one of them she has a slope in her backyard covered with it. Most groundcovers do spread pretty aggressivly. If it were me, I would fill the spot with daylilies. They are hassel free, and once established the foliage is nice, not to mention how many colorfull tropical looking blooms you could choose. Plus they will keep the bank from erroding. Sorry about the spelling. They spread but slowly and after a few years if they do need dividing you could give them to friends or sell them on the lily auction! Check out Maryotts for daylilies, they are in California too.

Thought I might share with you some of my favorite daylilies, enjoy
Smokey Mountain Autumn (nice fragrance)
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Awesome Blossom (evergreen would do well in your area)
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Frilly Bliss
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Dwarf mondo grass (Ophiopogon japonicus 'Nana) or baby tears (Solierolia) would work in a somewhat shady and moist location, but there are scores of others. Visit a local garden center to see what they have on offer.