It would seem that if you shorten the critical path, you need to spend MORE money (overtime, extra labor, express shipping, etc.), not less. So how could it save money?

Critical path and critical project requirements could indeed be separate issues. This is why you need to determine Priorities (Constrain, Enhance, and Accept) as we discussed last week. Assuming that time is the constraint, what are some things we could do to shorten duration (and cost, if possible)?