Earlier quoted context omitted.
The problem is once it's at the cell carrier level it doesn't even matter if you use a dumb phone. They know roughly where you are based on tower triangulation.
Not my area of knowledge at all, so perhaps someone who knows radio better could chime in: Would it be possible to fool the triangulation from the device, by arbitrary (or intelligently) delaying the mobile radio signals? Or are they too dependent on timings and such to work?
Expanding this, you could have N directional antennas pointed to N cell towers, and some individual delays on each of those antennas, it might be possible to fool the network triangulation. Such a setup would look highly suspicious if you were carrying it around, and it definitely wouldn't fit in your pocket.