Update: Dealership opened up a PUMA case, and after a few days, the dealership was sent updated software.

They are keeping the car overnight and will check morning startup. I discussed with the SA that there's some "quick" fixes such as the increase in idle RPM to 800, which may fix initial cold start but will make daily driving worse with jolting/bad shifting. He's not sure what the software reset will do, and said he'll let me know if this was part of the programming.

We'll see - but I personally don't think it's a software update. If I shut down the car right away after start when cold and restart, the engine is still rough - which would suggest to me it has to be a component vs. temperature issue, not a software fix. We'll see!