I think @endy is pretty on point here.
Whatever you decide, requiring your student to either take a zero on the assignment or drop whatever she’s doing for a last minute, unscheduled make up strikes me as unreasonable and unfair.
Is class ranking important at your school? If not, I don’t totally see how a potential bump in her grade has a real negative impact on your other students.
Does your school have a system for electronic submissions you can use in the future?