So I read a lot of these posts but my Prius IV seems to be different, I live in Atlanta, GA so it rarely gets cold and when I live in central VA I would experience the warm up cycle. My car has around 160k miles on it and for the past 30k miles (give or take) I have had a jerking sensation when the car switches from gas to electric. It is a stronger jerk at low speeds and more like a shimmy at 40-50 mph. It has progressively gotten worse with time, I mean it's by all means drivable but I have been trying to figure out what could be wrong before it has to be replaced and I'm on the side of the road.
This sounds like a EGR (exhaust gas recovery system) issue, and your mileage is about right for it too. I am not good at DIY but I know some have cleaned it themselves. Do a search here for gen 3 EGR problems