Well, there are lots of ways to do this sort of things, but I think your constraints have eliminated most of them... :-)

You don't want to call "df" and you can't install a module that would call the system call that "df" uses.

You've got to communicate with the OS somehow.

I say just write the file, and if the disk fills before you're complete, erase it and output an error message. (which you have to do anyway in case the disk fills up after you check the disk space but before you write your file).