I'm sorry to waste everyone's time, especially @logicito. But, I cancelled my Genius Bar appointment again.
I was unable to reliably demonstrate these issues just an hour before my appointment.
In preparing for the appointment, I rolled my iPad's version of iOS back to 9.2.1. I was running the public beta of 9.3, and I didn't want the Genius Bar employee to blame the version of iOS I was on.
After I was back on 9.2.1 and set up the iPad as a new iPad, I'm not getting any app skips. I am getting some pauses in my ability to switch apps immediately after using the cmd+tab shortcut. That doesn't seem abnormal to me.
As other people have said, these issues may eventually resurface. If they do, I'll set up another Genius Bar appointment.
Sorry again to waste everyone's time.