The system needs to be able to comfortably go quite loud for late night classes.
Why would late night classes need to be louder than any others? Given many of the other similar past discussions here, might you encounter issues with the resulting sound levels at neighboring businesses or residences?
I'd personally look at some of the recessed ceiling mount products from companies like Tannoy, QSC, Atlas Sound and so forth. I understand you want to avoid cutting ceiling tiles but you wouldn't hang the Quest Hpi boxes you noted from the suspended ceiling grid, they'd have to be mounted to the actual building structure above so you'd be cutting tiles anyways.