There could be a ton of reasons why someone can't put it in their house during this highly stinky phase. Teenagers, paranoid wife, trailer park, apartment, dorm room, lots of visitors including in laws, the list goes on.
A shack sounds cool. A tent may work. Ropes and tarps if made with a ridge so water can run off them may do the job. Renting a U-haul trailer could be the ticket if you clean the thing out big time when you are done. I wouldn't put it in someone else's house though for several different reasons.
One thing I would be concerned about with some of those options is how much light is going to get in (cuz you need it open somewhat for ventilation) and if that light is going to have a huge detrimental effect. Lack of moisture control or a hard freeze could both be issues too. Maybe someone else could elaborate more on the light, moisture and freezing while drying/curing topics. I am curious about those.