How To Steady Idle?

I am sure other more qualified will respond, and this does not answer your specific question, but all prii I have driven in (3) have a stage where they idle rough.
When they are in between being cold and sufficiently warm, the motor idles rough, sounds a little like a diesel, and shutters before shutting down.

 

Unless you get a check engine or other warning light this is completely normal. Don't try to defeat normal operation.

 

See The Five Stages of Prius Hybrid Operation. Once fully warmed up to above 73ºC, the car starts looking to do an idle speed check. It won't switch the engine off when it's running, and the car is travelling below the EV speed limit (34mph). It can't actually perform the idle speed check until you slow down to below 6mph and let the engine idle - so don't press the accelerator at all. This idle check takes 10 seconds from the moment the car goes into idle. For some reason the shutdown after completing the idle speed check is very, very rough. After this, though, engine startups and shutdowns are very smooth.

It seems to need an idle speed check once per driving cycle. Once complete, it appears to run the engine at lower speeds when engine demand is low, leading to lower fuel consumption when cruising.

If the car is travelling faster than 34mph, it will cut the engine as you slow down (fuel cut over 42mph, total stop below that speed). Very occasionally I've seen it start the engine to do the idle check when dropping below 34mph, but often the engine stays stopped.

I don't recall the engine ever staying on for as long as 30 seconds once warmed up, unless the cabin heater is set to a particularly high temperature. Cabin heat comes from hot engine coolant circulating through the heater core in the HVAC system. It's also possible that you had high electric demands, for example running the air conditioner to cool the car.