Embrace woodland planting, which can be lovely and lush. I have a tiny private south facing front garden (Scotland, so not scorching) which is my "new perennials" project, and a shared north facing back garden, and the latter is a bit more rewarding as a gardener. Mine is quite damp shade btw - dry shade a bit different. Get Beth Chatto's book on woodland gardening, for starters.
I especially love (interspersed with less showy plants!)
Japanese anemone Honorine Jobert's white flowers leaping out of the semi-shade (plant en masse, or wait to spread, which they will)
Rogersias (I love big-leaved plants - I have aescufolia and another one)
Primula vialii, really vivid red and purple for a shade plant, but elegant with it due to the long stalks
Brunnera Jack frost, I was initially sceptical but someone left some on a kerb for free, and now I love the white detail against more monotone greens of other plants
Japanese forest grass for texture and a lush, wafty feel
If I had a more grand garden I would also plant Fritillaria crown imperial like Beth Chatto did, but they'd look a bit gaudy here