According to this site specific to Vancouver island, Phlox diffusa is a possibility for you. It grows only 3-4 inches tall, has very pretty flowers in the spring, and, from a "lawn" aspect, has narrow grass-like leaves. According to some sources, it handles both rocky and moist soils but does not do well in clay. It seems to be a Western cousin of the Eastern Phlox subulata, which may also do well for you.
Other options include the creeping thymes (Thymus serpyllum and Thymus praecox), although like the Phlox they won't do well in clay. Because the leaves are scented, they do not attract rabbits. The creeping thymes are about 1-2 inches tall when not in bloom and 3-4 inches tall when blooming; the flowers are typically pink or rose-colored. Although there are some cultivars that you could use, your best bet from a cost and installation point of view would be to get seeds of the species, if you can find them.
Note that all three of these plants require good drainage. If you install any of these plants, once they've become established you may want to mow them after blooming to remove the spent flower heads. This will show off their foliage rather than the dried seedheads.
One other note - regardless of the groundcover you choose, if you have to walk on the site when that plant is in bloom, wear shoes because the flowers will attract bees!
