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I did the same thing recently, and had the same problem, I remember when they first came out there was a good post on Stratics showing you how to do it, but I cannot find that now.
It's all about the Interior Decorator tool. I think I placed and locked all the parts, on top of each other, but all messed up, then raised and lowered parts until they worked, the green bauble on the top being the hardest. I can't actually remember it was a lot of trial and error, I had problems with the bits falling into the container, so I may have done the other bits first and raised them, then slipped the container in underneath.