I think the free software community would get much farther if the acknowledged the realities of school districts with limited IT staffing. If you have a team of 2-4 IT people to manage hundreds or thousands of kids, you don’t want any software solution that doesn’t come with some form of tech support or at least some readily available help documentation or tutorials.
The biggest thing FSF could do is make a push for making the software as easy to use, troubleshoot, and understand as possible. Once it becomes less work (not necessarily less cost) to use free software, the change will follow organically.
Trying to petition schools to use free software on ideological grounds is a step in the wrong direction. Tie your movement to real-world incentives, not abstract ideology.
There is a metaphor with Islamic finance somewhere here.
If FSF wants school administrators to change their behaviour to stop using proprietary software, they'd need to make that change easy. If _they_ say that free software is too hard to install/use/manage, then the FSF can either:
A. Call that an excuse, which is a path of mutual distrust that will block change.
B. Listen more deeply to their underlying needs, then change their software to meet those needs.
C. Option B, then listen to themselves to understand what would make it easy to make that change.