As students it can be easy to ignore your health and develop bad practices like your friend is doing - in an attempt to salvage a failed project. I feel the true answer is to explain to them what I've written below, and that they need to stop over-working immediately - even if it feels wrong, or like they are letting the team down.
This project is being mismanaged
Despite what you may feel on a project that is so important to you, with so little time left - it is very important to recognise:
Crunch is not a necessary evil
The truth in all professional development is you have a fixed amount of time to make something, and a fixed amount of resource (man-hours) to make it with. The area that can change, is how much of what you wanted to do - actually gets done (the project scope).
Crunching, as your friend has been doing - is a failed attempt to rectify bad planning and management decisions made earlier in the project. They are trying to add more resource, to avoid changing the scope of the project. This is neither sustainable, nor good for their professional development.
It may feel completely crushing to accept this truth; that the project is not going to be delivered to the standard you wanted. But you need to explain to your friend, and colleagues, that it is not their fault you are in this situation - it is the fault of bad planning throughout the project (due to lack of experience - not malicious intent).
For this project to have worked, decisions earlier should have cut features repeatedly until you knew your goal could be delivered through sustainable development. Importantly, this isn't a one-off cut, this should have been on a regular basis to re-evaluate what goal was actually possible.
How to pivot and fix this one-off situation
So I do understand that it's one thing to tell you what went wrong, and how to explain to your friend that it isn't their fault this situation happened (and that they are not responsible for fixing it). But at the end of the day, you are still in the situation and do need to fix it however possible.
To try to salvage whatever you can, I'd recommend you take the following steps:
Identify how much resource you actually have, without overworking any single person. If it's just the one person for 6 hours, that's fine - it's what you have. Do not allow anybody to try and pull off a heroic last-stand. Everybody is to sleep - that is not their choice to make.
Identify what the most important features are that are on your backlog. List them in a priority order, cutting anything off the list that isn't a "must have". If it does not prevent you delivering - do not include it.
Estimate each of these tasks as a team. Whoever is available to work on that last section must be involved - it is their estimates you will be using as they are the ones actually making it. Double the estimates they give - you have already proven to under-estimate work as a team; do not expect that to change overnight.
Drop any tasks that do not fit into the time remaining. These are not to be considered under any circumstance - even if another task took less time than you thought. You are aiming to only finish these pieces of work and then deliver.
Assign the tasks and begin working. Whenever somebody finishes their tasks - they either help somebody else if needed, or stop working altogether. You do not want people adding scope in the last hours - you are aiming to achieve the new goal you've set and no more.
To re-iterate, you must first accept the project failure is not reliant on this person and explain to them how it is not their fault.
Secondly, you need to make a new plan that can salvage whatever is possible in the remaining time - given a sustainable effort to finish.
Finally, you need to act on this plan and accept that whatever the result is, is the team's combined result - not due to one person failing to pull their weight (proper management of the project would prevent that ever being a possibility).
Doing this, you will develop healthier professional practices. Failing to win the competition is a better outcome than solidifying the unprofessional mindset that anything can be fixed with more time/resource. Which IMO should be the most important factor as a student.