We get a little to carried away with our - no it can't be done - answers and sometimes forget the alternative ways of getting into Japan..!And this is a case of the alternative plan being an alternative for a reason.
Student visa are inherently expensive for the reasons given by Sira, and this just isn't an option for the OP. Not to mention that you can't support yourself, or pay tuition, on the 20 hr a week working limitation. Unfortunately, he simply doesn't have enough money banked already to make this a viable plan.