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I used to make schedules with aSc TimeTables years ago. There is a free demo available. Could you compare your approach with this app?
The application is fully automatic, in the sense that you first enter all the data and constraints, and then you run the computation. (There is an option to put some items on specific place and "lock" them there, but this is strongly discouraged unless you really know what you are doing. Essentially, you can do it to speed up the computation if you have a logical proof that certain things must be done some way, but the application can't notice that and keeps wasting CPU time with alternative approaches.) As far as I know, the numbers of teachers / students / rooms / subjects are not limited, but of course their number has an impact on the complexity of the computation.
The complexity of constrains for each student or teacher is much greater with our software than with aSc. The scripting language is much more complex and enables you to describe pretty much every whim one might have. Like a different speed, teachers have between two different locations or after how many classes a break is mandatory for a specified teacher ... and many more.
It's student oriented primary and every student can have a very different curriculum then everybody else.
Still, all this will be automatically calculated and then optimized.
Now, we want to see how it will behave in practice for North America and Australia.