Any suggestions as to how I would clean the inside of the tube to get the corrosion out, if any?


You can make a cheap disposable flex hone by carefully slitting a small wood dowel and sticking some emory cloth in the slit. You may need a zip tie or two if the dowel splits. leave enough cloth so it acts as flaps, chuck it in a drill and run it up and down the inside of the tubular (clyindrical?) part. Clean it out and try the quill again.