It is UNQUESTIONABLY a software / firmware issue. If it was hardware, the speakers would work or they wouldn't. If it was a dockingbay issue it would work or it wouldn't. I bet if it was possible to find the lot numbers of the components of our phones, we'd find something in common. Something in the component doesn't get along with the new iOS, so yes, a new component could fix the problem. However, the problem is rooted in the iOS not the component itself. Though I suppose it depends on how you look at it, now that I've typed all that out.
Anyway, I called support today, they deny any knowledge of this as a widespread issue (which I don't blame them for, they need to keep their jobs.) They are shipping me a new phone tomorrow, to arrive on Tuesday. I bought Apple Care + when I got the phone over a year ago, so I'm happy with that - no charge for the exchange.
I'd suggest that people with this issue call support. No matter how frusterated you are, be polite and just explain your situation. Odds are, you'll end up with a replacement.