It sounds to me like your problem is the media itself. I have the problem of transfer disks as well--I do work on a Plus, have to transfer it from 800K to 1.4MB disk on a Classic, and then use the 1.4MB to get the document into the MacBook. (Then I have to reformat it again since it's an ugly RTF file).

It seems a combination of age and use has gotten to these disks. The best suggestion is to just buy yourself a box of floppies.