Moving houses right now is pretty darned hard, especially for newer players who don't have a bunch of bags. Unless I missed something obvious, it seemed my only option was to take a pile of stuff from the old house, dump it on the ground in front of the new house and hope someone didn't steal it, then rinse and repeat a bunch of times.
The idea is that you get to rent a moving cart or some extra large container for maybe a very short period of time, say 5 or 10 minutes or something, just long enough to move your stuff, before the cart expires and goes poof.
I'm assuming there's some issue with the house knowing the contents you've dropped on the floor and that's why it doesn't just automatically transfer your stuff as it is, which of course would be the better option. ;)