I think icon has the issue covered.
I would address the walking out the door part. Usually a cat sneaking out the door has nothing to do with how she is treated in the house. Cats are territorial and exploring usually means they have observed the space long enough for them to feel they could stake it as their own. The excitement of you and your gf returning might also embolden Moon to explore a bit. The problem is the more Moon does this, the more she would feel like this is the way things goes, and venture even farther. So if you do not wish Moon to go into that space, try to use your legs, bags, purses to form a barrier and gently shuffle Moon away from the door.
Another possibility is that Moon has been seeing other cats or animals outside, and she feels like her territory is being trespassed. So she might want to get out there and reclaim the area. Usually this is less likely to happen for spayed or neutered cats, but some cats really care about their territory. If that's the case then there are two ways to approach this. A. Prevent those animals from getting inside of her territory, which is super hard to do in a urban environment. B. walk Moon on a leash around those areas, so she feel secure about it, which isn't possible at your present situation. It's the more unlikely scenario anyway.
If the room mate really doesn't have time to clean after Moon, maybe her rich boyfriend could afford to buy a self-cleaning sandbox. If he is really rich, tell her to get the catgenie. It needs to be connected to a tap water supply and a sewage drain.
It's not ideal... but it's better than Moon's sandbox being dirty for a whole week. By the way, the ideal number of sandboxes for a single cat household is 2.