I just want to make sure I have this clear. Without using sessions you need to pass variables through a FORM.
1) User inputs data and presses submit
2)Variables are passed to page x
3)Page x is not displayed to the user and has no submit button?!
4) Page x points to page z
5) No vars on page z
Why not call all of page x as either an include or a function of page z? I Am not sure why you would want to do this in tewo seperate PHP scripts?
if you add the line
inlude(x.php) ;
before any of the code on z.php it should work fine