I've searched high and low, and I'll be jiggered if I can find an answer.

I'm going to guess your plants have it too good, and would benefit from some stress to make them feel threatened enough to flower out of self-preservation. Uniola paniculata lives and thrives in some seriously adverse conditions, and seems to flower just fine. Perhaps the garden setting is just too easy for it.

Don't feed them at all. Cut back on watering them. If you can work some sand into their soil without damaging the root systems, try that.

thank you Donn,

i just added a bucket of shells from the beach around each one, we'll see

Mine always bloomed & set seed when I lived in Long Beach, CA.
It was in lightly dappled shade.
Watered only once a month.
No fertilizer.
And self-sowed.

Perhaps you're taking too good care of it.

I used to have some and it bloomed regularly, on its own. It was in clay soil, little fertilizer and occasional water. Partial sun, mostly shady. The city has planted some at a couple of bus stops and they bloom all the time, and I know they don't get any help at all.