To be very frank, I would cancel the room here and rebook two rooms somewhere that has availability. Or not even bother crashing those few hours.
Aside from the squeeze - and believe me it will be a tight squeeze - just having to take turns in four at the bathroom for a shower would be enough to put me off. 10 minutes each? That is already 40 minutes out of the sleep time you have calculated

Personally I would never sneak in someone in a hotel room, not for any moral reason but for a very practical one. If something happens - incident, theft, whatever - that person does not exist and can bring no claim.