All institutions request that you obtain letters of recommendation from people in positions to comment on your intelligence, work ethics, skills, and potential for contribution to the field. Advisors to St. Mary's Projects can be excellent candidates, but in general it helps to ask faculty to know well. Schools will want to know how long and in what context recommenders have known you. Above all, be nice to your recommenders and thank them afterward. Admission and financial aid decisions are often made well in advance of stated university deadlines.
Departments are often free to set their own deadlines, independent of the university.
So double check. However, don't compromise the completeness of your application package. Be aware of the deadlines and make and educated decision. Apply for Fellowships. Many fellowships exist to fund graduate students in the sciences, particularly those seeking Ph.D.'s.