Quick update: The dealer received (ordered?) the wrong part, so no news on whether replacing the screen would help.
In the mean time, I've continued to wait at least four seconds between unlocking the car and pressing the start button. So far, so good: no frozen screen issues.
The only exception was one time when I had left the car unlocked with the stereo on (my wife was in the car). When I got back into the car, I pressed the start button right away and the screen froze. As I understand it, there's some question as to what prompts the system to start up: pressing the unlock button or pulling the door handle open. In this case, I didn't press the unlock button at all, and I hit start the start button almost immediately after opening the door. So either way, the system would not have had a chance to finish starting up.
In the mean time, I've continued to wait at least four seconds between unlocking the car and pressing the start button. So far, so good: no frozen screen issues.
The only exception was one time when I had left the car unlocked with the stereo on (my wife was in the car). When I got back into the car, I pressed the start button right away and the screen froze. As I understand it, there's some question as to what prompts the system to start up: pressing the unlock button or pulling the door handle open. In this case, I didn't press the unlock button at all, and I hit start the start button almost immediately after opening the door. So either way, the system would not have had a chance to finish starting up.