I doubt that there's any way to fake location based on cell towers. That's all done in the baseband radio, which is not readily user accessible. And even if you could mess with it, it's probably very illegal. It's certainly illegal to spoof mobile subscriber identity (IMSI) because that allows theft of service.

It's much easier to disable GPS location capability. But even that's not very reliable, because there are multiple software levels, most of which aren't user controllable.

The best option that I know is turning devices off, and keeping them in Faraday bags, except when in use. So you get to pick which locations get reported. You're less reachable, but that's a necessary tradeoff. For long-term storage in Faraday bags, it's important to remove the battery, because otherwise the device may drain it, trying to ping towers, even though "turned off".