We're in the new place with zero furniture.
Fortunately, there is an Ikea close to a train station. It's still not easy, but it is possible to buy rolled up mattresses from Ikea and hulk them from bus and over two train rides to get them home.
|Shrink-wrapped mattresses from Ikea|
The trains here are wonderful. Beyond having space enough for us to lug home two mattresses, they run ridiculously often. The longest we've had to wait was 20 minutes for the most direct route. Shorter waits were available, but less direct. Usually, it's less than a 10 minute wait for the train we want.