Tate,
It sounds like a case of gummed up oil on the ZZ parts. I'd Tri-Flow the dickens out of it.
As for the plastic case, be very careful, remove all the screws, knobs and other obstructions, look for hidden screws and tabs, then carefully separate the halves. Yes, you can break the plastic pretty easily. I've never had a Kenmore plastic machine apart, but I did have one Singer apart. Just pay attention to the way it's assembled and don't force anything.
Joe