Answer: The site you describe is a real challenge. You may have the best results by planting in containers and swapping the containers every 2-3 weeks!
Phormium will not be as happy in part shade as Japanese Blood Grass so you might try this plant. Or, you might consider Berberis thunbergi atropurpurea 'Nana' (Crimson Pygmy Barberry). This plant grows 2' x 2', has purple/red foliage and will adapt to either sun or part shade. Japanese maple would be a final suggestion. There are many cultivars, some with lacey foliage in a deep burgundy color. You can prune these to keep them small and they love growing in afternoon shade.
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