I'm not from Madison, but here's what I'd do.
1. Retain a lawyer, or at least get a consultation (usually free);
2. Print out the relevant documents;
3. Take a firearm you don't mind being confiscated (iow not your Commemoration gold embossed 1911)
4. Take a friend;
5. Run a video and two sound recorders;
6. Consider CC and make sure you have your permit;
7. Park off grounds and walk to the school door (?) this is to avoid a 'parking lot' or a 'traffic violation' and the extra powers LEOs have when you're driving;
8. Dress nicely, black clothes, black gun, they may not see it;
9. Be aware of boisterous teens who might make a scene if they see you.
Good luck!
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e6chevron: Can you produce a cite? I could only find stuff from 2000 and 2006. MOST schools allow you to CC with a permit IN your car where you remain while picking up/dropping off kids. Isn't Madison the same? Also, beware of local regs, if any. Maybe call the school or the PD and ask anonymously?