Is it required by the California EDD to hire people as W2 employees for this case or could I just employ them as contractors? I wonder how companies like TaskRabbit and Uber are able to employ people as contractors with California EDD's "temporary service employees" regulations.
You can indeed hire them as contractors and avoid bringing them on as employees. CA has guidelines by which the EDD decides if the person is a contractor, and here they are:
In your case you pretty much satisfy all of them. So you have nothing to worry about and can hire them as contractors without risk of being audited by the EDD.