What example could Iran look to where a theocracy managed to stay in power and raise the standard of living of its inhabitants while maintaining power?

I’m not sure people at the pinnacle of power care much about previous examples. Some do, surely, but we are seeing many even today who could give a rat’s patootie about such niceties. And throughout history we have dozens, even hundreds of different forms of organization and power. We have Kings (usually with religion) and Pharaohs (who were the embodiment of their religion) and real theocracies such as was practiced in the pre-European era of Central America - and all of which did OK by their people, judging from the pyramids and landmarks they left behind.

Religion has been a central organizing force for humanity throughout history, the irony of course is that each one believes it is the “one and only true religion”, which causes the formative us/them conflict that so often brings it low. From the Roman gods and Egyptian empire to the Japanese Shinto which strove to anniliate Buddhism and spawned the extreme militarists of the early 20th century.

Iran’s theocrats have power. Don’t expect them to think too deeply about what they might do better if not they had less. They’re more concerned with holding on to it - as everyone in power anywhere and for all time is.