I have been that person.

I know what it is to be over eager, over achiever, liking the work and having a deadline.

Let me tell you what happens when you try to slow down that person:

It looks like you are doing it for your own interests. (as you said, "it makes us look like shit")

It's obvious.

What does he get? He is just (from his pov) increasing his chances of survival, and in his mind you want the opposite, so he works EVEN MORE.

So, you need to MAKE IT ABOUT HIM, show him WHAT HE CAN WIN. (by slowing down)

How to do it?

You need to tell him something along these lines: (add whatever context/rethoric you want)

"Would you like to grow in your career? Become a senior or more senior? Achieving it involves your ability to influence. Would you like to become eventually a team leader? Would you like to become the expert that many people want to follow?" (All these questions should be an obvious YES) (To double confirm you can ask probe questions like how do you see yourself in X years or so, and modify the questions accordingly)

"To achieve that, you need people to want to be with you, to follow you. Right now the team is worrying about how are we perceived, and by having a source that is impacting on our perceptions as a team, it makes it hard to build that trust that will allow YOU to influence eventually, so we not only need to consider our output but how our team perceive us. Let's plan AS A TEAM, to commit to deliver only X by time Z. YOU WILL WIN everyone's alignment and also get that (X on Z) achievement"