Ah, I think we may be talking cross-purposes.
My issue was that I had no GPS signal at all. You obviously need greater accuracy than I do.
Before the SIM trick, I had zero GPS signal according to the GPS Diagnostic app. The SIM trick restored the A-GPS function on my iPhone X, giving me 10-20m accuracy according to that app (about the same as your 16m mentioned above). However, for comparison, I just tested on my wife's 6S. She gets the optimal plus/minus 10m reading on it! I think my iPhone X has been slower to get the initial position lock, and less accurate, than my old iPhone 6 and my wife's iPhone 6S from the very beginning.
I also noticed that the Altimeter reading in the Barometer app is less accurate than on hers. I think this also affects the three dimensional positioning you referred to:
"Barometer: You might think of a barometer, which measures air pressure, as primarily a weather-prediction device, but it's not used for that purpose on an iPhone. The barometer supplements the GPS chip for measuring elevation changes to create more accurate elevation and elevation-change readings."
https://www.lifewire.com/iphone-gps-set-up-1683393
PS: I agree the Compass function is probably irrelevant in your case, but some sites recommend it, so just to rule it out, I would double-check your Compass is set with True North on, i.e. not Magnetic North (Settings, Compass, True North) and your Compass Calibration is turned on (Settings, Privacy, Locations Services, System Services, Compass Calibration)