Met with Apple Genius earlier today and ultimately received a replacement iPhone 7 Plus.
My old phone was officially replaced due to a faulty GPS chip.
But before the tech erased and reset the device to check the GPS, I told him about the Bluetooth stuttering. I brought up my video and showed him 2 printed pages from the beginning of this thread.
He ignored the video, but read through the printout. He quickly -- and confidently -- stated that the issue was due to the iPhone 7 using a new Bluetooth chip and updated Bluetooth protocol. He said that most older car audio systems need to be updated to work with the newer Bluetooth.
I probably should have asked him whether the car audio systems needed a hardware upgrade (aka. replacement) or a software upgrade. And I probably should have grilled him on why Apple chose a chip and/or protocol that was incompatible with the majority (?) of cars on the road.
But it either didn't occur to me or I thought the questions wouldn't have been productive. It was also extremely crowded and noisy.
Anyway... when I asked him for an unlocked replacement, he confirmed that my old 7 Plus was in fact already unlocked (I originally paid for the device outright).
So after about 90 minutes of restoration, I connected my replacement unlocked, 128GB iPhone 7 Plus to my 2011 Prius and drove home. The first 15 minutes were glorious. No stutters or drops while streaming Apple Music.
Unfortunately in the last 5 minutes, I switched to the Reminders app to create a to-do and that's when the stuttering came back.