So far:
I've gone through 3 8 plus phones, with the third one ultimately being captured by Apple. I've logged data, answered every question asked of me, and been cold-called from this thread by some direct group of engineers who work on the software updates, etc.
I replaced it with an iPhone X which is showing signs of the same problem. Thus far, engineering has no solution. It's that simple. Every indication I've gotten is that they don't even know what's really the problem yet as originally it was thought to be a software problem, but capturing my device indicates they think it might equally be a hardware problem.
The new data point of it happening on a brand new X creates a whole new headache since it would appear to me as a layman that the issue is clearly hardware and some faulty design based on the glass back. That said, I know anecdotally of people who have had the issue on pre 8-series phones after upgrading to iOS 11.
Since this thread is followed by a ton of people at this point, I'd be curious to know where folks stand on what I think is the culprit, which is some combination of a very specific environmental factor and the hardware design of the phone. I say this because I cannot for the life of me recreate the issue in one of the two cars I own, while in the other I can't drive to the store and back without the issue (a Hyundai)
It would suggest to me that those of us who have been beating our head against the wall with this are in some bizarre small group of people who's cars, or something else that Apple didn't really vet, are interfering with the GPS signal. Could be a part of the car, maybe certain satellite radio antennas, maybe something you carry on your keychain like an RFID key. Whatever it is, it seems to me to be something environmentally specific that is like getting through to the device through the glass back in a way that was never intended.
Those are my thoughts after dealing with this for going on over a month and 4 phones with no real end in sight. The annoying thing about it is, for all the inconvenience and time spent on this, it would take me even more time and energy right now to spend literally moving everything over to a new OS, but that point is approaching.