Of course, short term contractors are ideal for overflow work. My point is that I try not to rely on part time contractors over the long term because their availability can change.
Speaking as an employer, availability is important. If you're only working 15-20 hours a week for me, you've surely got other commitments that are occupying your mind and time. I've also seen many people doing part-time contracting take on more than they can handle, either moonlighting part-time from their full-time job or taking on too many simultaneous gigs. I've done this myself as a contractor, so I understand why it's happening, but as the employer I don't want to be on the receiving end.
I still hire part-time contractors for things, but for anything that's time sensitive or availability is a concern, I prefer to have a full-time employee.
I second this comment. Your chargeback request needs to color neatly within the lines of their procedures if you want a smooth process. How you phrase your request is incredibly important. Do not go crazy on details specific to the situation, use a template.