Ask HN: Motivitating employees to work harder through project bonus?

I lead a remote team and give each individual the flexibility to choose their own working hours and capacity—"your work speaks for itself", etc. We're working on a long-running software project with a deadline that's fast approaching.

I want to ask my team to work a little harder to meet our goal. However, I find it unethical to require people to work overtime, in return for pseudo-glory or empty promises of growth. I want to instead reward them with something tangible.

I'm considering a project bonus: if we ship by this date, everyone on the team gets $X USD.

However, I'm reading that money isn't always a good motivator. I'm wondering if anyone has experience with this, or any other strategies for getting teams to work harder than usual without encroaching on their right to live and work on their own terms.