Is there a way to determine how cash in the bank will effect the FAFSA score? I would like to put some of our cash down on our mortgage to decrease our cash on hand, but I don't know how low I need to get the cash balance to help our FAFSA score.

You cannot really tell how different things will affect your FAFSA, but FAFSA 4caster is a great tool: http://www.fafsa4caster.ed.gov/F4CApp/index/index.jsf
It will give you a better idea of what to expect.