Depends how big the whole area of the yard is whether you stick to one plant only or not - I wouldn't, I'd use probably 3 different plants planted in groups of at least 3 or more, depending on the ultimate size of the plants chosen. It won't be easy to achieve the layered effect you want with planting because the border looks to be quite narrow, and particularly narrow in the middle part, where the paving curves. It's probably best to stick to group planting along the area.

The Rhoeo spathacea 'tricolor' in the photo (your Moses in the Cradle) should work there, though it does colour better with some sun - I suspect it would go quite plain green in full shade. Liriope is definitely one to consider - common name Lily turf - there are variegated leaf versions available such as L. muscari 'variegata' or L. 'Silvery Sunproof', and it produces short stems with lilac flowers.

Chlorophytum cormosum (Spider plant) would be good, but it doesn't like to dry out all the time, so that might mean it's not a good choice if you can't keep it watered as necessary.

Brachyglottis 'Sunshine' might work (sometimes still called Senecio greyi or Brachyglottis greyi) - I'm just not sure whether it would cope with the temperatures in Zone 10b - it does grow in other parts of California up to Zone 9b, so might be worth risking. If you risk planting this one, it gets taller than any of the others I'm mentioning here, with a similar spread (can be clipped or shaped once or twice a year to make it rounded if you want), so care should be taken when positioning it. Responds very well to trimming, shaping and hard pruning. Its grey foliage would make a good backdrop for that purple leaved Phormium or Cordyline I can just see the edge of, bottom right in the photograph...

UPDATED ANSWER:

In light of the new set of photographs you've posted, and your suggested plantings, I hate to be the bearer of bad tidings, but I doubt any of these will work. The area is shady - bougainvillea, for instance, needs a minimum of 5 hours direct sunlight to flower successfully, and it needs a framework to climb or be tied to, so I'm wondering what you were thinking of supplying for that. Second, the ivy next door is a big problem - in Photo A, you show a new bed outlined in red where you're thinking of planting Hibiscus of some variety and the Bougainvillea - if you open up the ground there and plant into it, the ivy will spread into that in a heartbeat - its likely the roots are already encroaching under the 'grass' or lawn or whatever it is that's already there. Planting anything in that area will not 'keep back' any growth from next door, its topgrowth will continue its inexorable invasion unless it meets a solid object, when it'll climb up it (if its actually Ivy).

Equally, Cannas prefer full sun, or about 5/6 hours in hotter climates, and won't do at all well in no sun conditions, plus I doubt there's much root room to add anything at the base of the King Palm shown in Pic C, you'd need to try to dig around a bit, gently, to see how much 'free' soil there is available - there may be hardly any, which means you can only put very small plants in there.

Really, the only way forward is to look at shade planting exclusively - the roses need to come out, they'll never do any good with such low light levels. Nearer the front of the property, there is certainly more ambient light, but you have said there isn't really any direct sunlight even there for any length of time, which means that choosing shade lovers is probably the best way forward. One other option to consider is removing the King Palms IF that means some sun will reach the area - by doing that, you change the conditions and can then consider other plants. It does, though, seem almost criminal to remove them - I can't see the tops so don't know how attractive and healthy the foliage is, but the trunks in themselves are things of beauty. Note that your King palms like neutral to acid soil conditions, so you can assume that's what your soil's like there if they're growing healthily.