I showed up for my appointment, explained the problem, suggested that the screen protector was the problem and gave the phone to the tech to test. She came back in short order and reported that the microphone was indeed faulty.
The phone go swapped and it was covered by the manufacture's warranty, thus not counting against the two oopsies available to Apple Care+ customers.
I'm not that worried about not having a screen protector. I didn't want one in the first place. I bought it under pressure from Verizon. Yes, I was aware of their aggressive sales techniques. Yes, I rode bareback for the second year of ownership of the iPhone 4. And for the entire year of ownership of the 5S. (The 4 [iCall 1.0] was heavily scratched. The 5S [iCall 2.0] had some nicks around the edge and I think the screen was coming loose. But I think that had less to do with the phone not being in a case and more to do with the phone being in my pocket when I was laying on my stomach on occasion.)
So now it's a matter of waiting on the restore. And having to sync iTunesU twice per usual to get all the media to properly transfer. And hopefully, after all that, all will be well.