So the firmware password isn't the one I entered. To avoid the usual onslaught of insinuations that it 'might not be my computer' that usually accompany questions of this nature, I want to state unequivocally that I am not asking how to bypass it, I'm trying to figure out why, and what (if anything) I can do to restore the EFI so that the password I entered will work. It may seem like a fine distinction, but it's an important one.
The nearest I've been able to ascertain is that the firmware I'm running is not the right firmware for my machine/OS combination. I was looking through the list of firmware updates on the Apple website here: https://support.apple.com/en-us/HT201518 and it seems that I'm running a version that isn't listed. According to the site the version for my machine should be:
MBP112.0138.B16 When I look at the system information is says that I am running
Could that be the issue? If I flash the older firmware will it respect the password or will I still be out of luck?
So in my haste I overlooked the disclaimer on the Apple EFI/SMC Updates page stating "If you don't see a firmware version listed in this article, it means that either a firmware update is only available as an automatic update, or no firmware update is needed."
That answers the question.