Why not allocate more addresses to your subnets? There are over 65000 address in 192,168.0.0/16 and over 16 million in 10.0.0.0/8.
Why not (for example) use 192.168.0.0/18, 192.168.64.0/18, 192.168.128.0/18 (over 16,000 addresses each) 192.168.192.0/18 for further subdivision and future expansion (e.g 192.168.192.0/24 for servers, 192.168.193.0/24 for teachers's and admin PCs etc).
I can't speak for brcisna but most school network environments use Public IP Subnets instead of Private IP Subnets. So I'm thinking that is why they are running out of IPs.
The company I work for, we used to use Public IPs for our internal servers but over the last 3 years we have moved them to 10.x.x.x and re-use the public ip for any internet facing servers.. Then again Public IP space for my company isnt running low yet
Many higher ed institutions already have IPv6 allocations, it's simply a matter of architecting and deploying. Generally most have been too apathetic about IPv6 and now everyone is behind and scrambling to figure it out and port their old tools to support it and begging for money to upgrade infrastructure to do IPv6. It's really not that hard, especially for anyone that has done another protocol in addition to IPv4. For a long time our IPv6 path wasn't the same as v4, nor does it need to be, as its a totally different protocol.
Internet2 has a workshop that they put on (that I have been an instructor for in the past) that teaches v6 deployment / theory, etc. to networking folks.