Part of the challenge lies in the fact that Apple iPads are unbelivably stubborn about holding on to their signal when connected to one AP and doing EVERYTHING they can to maintain a connection.
Turning our power on both 2.4 GHz and 5 GHz to low helped a lot with this, and I also have the 2.4 GHz channel active on every other AP so we don't get too much of the rogue 2.4 GHz signal between classrooms. I've seen much more appropriate switching between APs with this configuration.
The issue I need to resolve is just the bandwidth maxing out, and I'm hoping uping the bandwidth from the 20 Mbps (both directions) to 50 Mbps (both directions) will resolve most of it and then I can fine tune from there. Our other campuses are on a 50 Mbps connection and aren't seeing this issue, with almost exactly the same network structure, and having learned last week that someone had decreased our bandwidth at this campus without informing anyone was a surprise.