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It's definitely doable, I've seen people go as high as clearing it with 30 seconds to spare :D You can do it! 

As far as I remember (it's been years, sorry, ahah), there's one item that can go under the bed, but the nightstand also work for that one;
I think the closet was meant to be a "catch all" - you can put anything in there and it won't result in a penalty, but you also won't be able to get max score if you use it... Not all places are meant to be used to their fullest, anyway. Gotta have some misleading things to mess with y'all. ;)