I also run a school-based network. I find that lots of software in the education market doesn't come in MSI format, so installing via GPO proves impractical sometimes. Most software these days does come with an executable installer that accepts "silent install" options - see AppDeploy for a site dedicated to figuring out how to get applications to install over networks.
WPKG is an application - a client that installs on your machines - that can be used to install and update applications on workstations. It's free and open source. You can simply write your own script to install software: I have an "install" user on my network, with admin rights, that runs a logon script that runs through the silent installs for a bunch of applications then reboots the machine. After reimaging a machine back to freshly-installed Windows just log on as "install" and let it chug through all the installers. This can be a bit fiddly to set up, so WPKG is probably the better option.
If you come accross an installer that's just plain awkward, or broken, or both, the excellent AutoIt can automate pretty much anything you can throw at it. It's a suprisingly complete Windows automation / testing utility, with good documentation and example code that lets you fake mouse moves and clicks, button presses, waits for windows with specific contenst to appear, pretty much any feature you can think of. It's also free.
Edit: If you want to completly avoid having to visit each workstation, you can create a script that runs the silent installers from a schedulaed task. Probably make the task run at 8pm or something, then turn the machines off.