OK, there is a slow flushing stool, tank type with a flapper. When you flush it, a burst of air comes first and then the water slowly drains. It is the style that has the hole to start action, and it is clear. The one right next to it is OK. There is one vent for 2 rest rooms, a water fountain, and a former restroom on the floor above with everything now blocked off. 50's masonry construction. If the vent is blocked between to 2 stools, how would I ever get to it? The vent isn't even over the wall the restrooms back up to.

OK, there is a slow flushing stool, tank type with a flapper. When you flush it, a burst of air comes first and then the water slowly drains. It is the style that has the hole to start action, and it is clear. The one right next to it is OK. There is one vent for 2 rest rooms, a water fountain, and a former restroom on the floor above with everything now blocked off. 50's masonry construction. If the vent is blocked between to 2 stools, how would I ever get to it? The vent isn't even over the wall the restrooms back up to.
... cleanouts sticking out from the wall? It may be a longshot but it is possible in this arrangement that a cleanout may be the closest thing to accessing the vent or the drain, for that matter. Might even be on the upper floor area.

OK, there is a slow flushing stool, tank type with a flapper. When you flush it, a burst of air comes first and then the water slowly drains. It is the style that has the hole to start action, and it is clear. The one right next to it is OK. There is one vent for 2 rest rooms, a water fountain, and a former restroom on the floor above with everything now blocked off. 50's masonry construction. If the vent is blocked between to 2 stools, how would I ever get to it? The vent isn't even over the wall the restrooms back up to.

Hey ,you have a partial clog in the drain, (not the vent) that's causing the discharge to bounce back pushing a bubble of air ahead of it. The only way to clear the clog is to pull the toilet and snake out the drain. Since the clog sounds close to the toilet you shouldn't have to put out too much cable to hit it. (that church oughta put you on a retainer! ) Have fun! Tom

Thanks for the answer. It sounds difficult, but possible. I may recruit a helper.