Are you looking for a shrub, or a perennial flower?

That's a tricky siting situation.....many more plants would prefer the reverse lighting conditions: morning sun and afternoon shade. Finding something that would be happy in more shade than sun yet still tolerate the very intense and hot afternoon sun is a lot more difficult :-)

Exactly how much room do you have to work with there? Drimys lanceolata is a possibility but does not offer a very showy flower.

Have you considered a large container planted with more seasonal color?