If you have an AP in every classroom, office and common area, I would turn off auto tx and statically set the 2.4ghz radio to no more than 5dBm. This is still more power than you need on each AP. I would actually recommend disabling at least half of your 2.4ghz radios but without doing a proper site survey and not knowing building materials, no one would be able to tell you how many to disable, which ones to disable and what power to turn the remaining radios up to.
The issue very well may be a co-channel contention issue. This will eat up airtime on the AP and cause high latency on the network. Because every channel is a contention domain, if an AP can hear another device on the same channel, it can not talk and must wait for the channel to be clear before it can send data. This causes data to queue at the AP and cause latency.
I would start with updating firmware because they have had a lot of buggy versions for what seems like 2 years now. Then I would get a print out of your floor plan and write down the channels the APs are on and adjust if needed. Co-channel contention is unavoidable on the 2.4ghz band, but if you plan appropriately, yo can minimize the effect it has on the network. After that, assuming you have one in every classroom, start turning them down to 5dBm.