If you don't have to worry about getting thrown in jail, I wonder why more people aren't doing it? ;)

Anyway, to answer the OP's question...is there some combination of POST options that loads the entire class schedule at once? I know my school's (U of Alabama) system had a form where you could select all of the course departments and load the entire schedule on one page.

Also, do you really need to reload the data so often? If the IT department is worried about server load, perhaps you could arrange to get a data feed once or twice per day (overnight would probably be best).