Is local jamming or removing their antennas a viable strategy? Seems like it could be easier to just make them unable to phone home, rather than trying to surgically rip out the bundle of hardware and software responsible for it while leaving everything else intact.

Vehicles differ. Disconnecting the antenna is easiest in some. Removing a fuse is sufficient in some. Disconnecting the relevant module is not surgical in some. Some nag if the antenna is disconnected.