Thanks again Barb - It is indeed the same device, though apparently not the original problems. I would indeed have exchanged it, but it was rather urgently needed (I was using it with the touchscreen disabled - until I tried the N-Trig tool). Now, after
a third reset, the original problem has gone, at least for now, the touchscreen is still fine, no BSODs for now, so it is just the GNSS sensor. Maybe this time it really is hardware. I'd still like to be able to do a "battery out" reset, though.
[EDIT] Well, very shortly after writing the above - Windows Update has automatically installed version 20.22.9057.18 of the Broadcom GNSS 47531 driver on my device. The previous version, which crashed on my device, was 20.23.8244.18 - in my case installed
from the latest Surface 3 LTE driver package "Surface3_4GLTE-RestOfTheWorld_Win10_151120_0.msi", though I believe the same 20.23.8244.18 version was also, at one time, on Update. So far this older version appears stable on my device, which for the moment seems
happier in all respects. (By the way, to clarify, removing the SIM only ever affected the first and most minor issue, the crash of the IA7260 Firmware Update user-mode driver: no effect on phantom touch, or GNSS crashes.)