The only thing I can think of, and maybe this'll stimulate someone else to think of something better, would be to make a copy of your form that shows the ten rows you want to print. Then on your four-row-havin' form, put a button that opens this other form (it could say "Open printable version" or something). Then print that version. It's not perfect, but that way you can have your ten rows viewable on screen only for this "print" version.
Not knowing the details of the form, it's hard for me to say if this will work, and if it'll work, if it's acceptable to you.
Good luck.