Had a rough cold start with violent knocking/shaking.

Probably not / maybe / not much.....

 

Same story here: only had this once, after engine had run just a few seconds, then car sat for a day or so. When it was shaking, shutting down and restarting stopped the behaviour for me.

 

idk whether they will help you, depends on whether or not toyota states that they have to experience it, or take your word for it.
but either way, the new manifold hasn't proved to solve the problem.
we don't know if it will do long term damage, but the best thing for you would be to not shut the car down when it's warming up.

 

If it does it again hold your foot/accelerator to the floor it makes it stop sooner.

 

Had this same thing happen twice with my 2010 with 86k miles. Both events separated by a couple years. No rhyme or reason to it. I just turn off the car and then turn it back on again, and all is good. Very strange...

 

2012 Prius V - rough start periodically over past 3 years. Vehicle generally garaged. Recently not garaged. Rough start more common. Smell of antifreeze in vent system. Finally throwing a code. In ship now for analysis
Head gasket and maybe head itself need replacement. 182,000 miles. Like the vehicle. Estimated cost $2,500. I think I'm getting a good deal on repair. Time will tell