This three-dollar bouquet of flower was the inspiration. They florists call it safari, but it's an Australian plant called Leucadendron (safari sunrise is likely the variety).
With only a tiny bit of research, that seemed to tell me that leaf-bud cutting was a good way to reproduce this species, I marched to the garden shop and bought 2 different kinds of media (to experiment with) and some rooting hormone. So now there are cuttings of the stems and leaves of this plant (which is from a bouquet and that may not work at all - who knows how many days ago it was cut) plus some fresh cuttings from plants already in my yard: fig tree, blackberry vine, and tea tree. Hopefully something will make it through. And to further confuse the experiment I brought some pots inside (the garden shop guy who helped me said they needed some heat). So we'll see how well any of this worked in about 3 weeks when I wiggle them up to see if there are any roots growing... Oh and I also cheated and planted a tray of some grounds cover that was already putting down starter roots.