I called Yaesu, and the technical rep told me to exchange it, if possible, for a new unit. I had already passed the 10 day return period (I would now incur a restocking fee), so that was out of the question. Yaesu told me to send it in for warranty repair.
My greatest fear of a touchscreen unit was realized - once the screen stops working properly, there's nothing you can do. In this case, the tech rep made it seem like the touchscreen was misaligned. He had seen the problem a few times. He assured me this was relatively common and easy to fix.
So now I wait.
I really like the unit, I'm just disappointed that this happened to mine.