Is running a fake cell tower technically against FCC regulations? Any possibility of just reporting them to the FCC and causing them to incur fines or take them down?

The people at FCC are just government officials. They'd be foolish to antagonize the leadership of the executive branch based on just principles (I know how unscrupulous this sounds. But such are times). Besides, they are up against one of the most heavily funded rogue forces in the world that is also known to go after people outside their jurisdiction (citizens) with impunity.