As I read Carrot's post I don't think he wants to carry there so much as take down the signs that prevent carry and make that school a "gun free zone" target for a lunatic. It's a bullseye for those people.
The GCA doesn't restrict permit carry in schools afaik and doesn't give schools special power to ignore state law on the subject. If state law says they can't restrict carry access I'd say they've got no leg to stand on.
Carrot, is your state Rep or Senator sympathetic to the pro-gun cause? They'd be my first stop. They would have the quick access to the legislative legal resources to answer the question of legality and also the ability to take action.
I don't see anything wrong with going to the school board either, very respectfully, and ask if this is board policy or if the school did it on their own. I wouldn't go to public war over it right then and there, just gather facts. I'd approach a member or two, not go to a public meeting. They'll be very defensive in that environment.
If it is board policy I might raise the issue that they don't have that authority, but not press it hard. Just gauge the level of resistance. Again, not in a public meeting but privately if possible, try to make it as easy as possible for them to not look like they're being pressured to a particular action.
It also keeps anti-gunners from grandstanding on the issue and trying to make it a referendum on "guns in schools", which is not the real issue.
If the school board is unresponsive and the legislators who represent you I'd contact one or more of the following 3: any state legislators who are champions of the gun cause, any state gun association that has been involved in lobbying and legal cases on the gun issue who may be willing to take on the issue, and the NRA-ILA. The latter two will take on cases like this.
try to keep it low profile to start, sometimes that can get action easier than a public display. If it's just the principle doing it maybe they can just be quietly removed and it's over, or the legislator can contact a school board official and work out a quiet removal. Your goal is just to get them down, not become national news. Just my .02, and if the nice approach doesn't work it doesn't preclude the tougher options like NRA-ILA or other lobby involvement.
I'm with you on not wanting the signs up. Has nothing to do with me carrying there, has to do with there not being a bullseye on the door.