I gotta agree with you, there definitely should be a Slice of Life genre. By the info you gave about your story, it seems that it’s a sequence of events where the situation is always changing (correct me if I’m wrong) and Slice of Life would be perfect for it. I’d say just keep it in Drama (I’m not sure what else would work) but I’ll definitely keep this in mind for whenever Episode comes out with an update. 
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