My condolences on the scratching. I know it's frustrating, especially when you go back into the collection and find scratches on your older negs too...
It's part of what put me off my Nikon F80 and encouraged me to look at different options for DSLR. My F80 would leave the same scratch, sometimes three of them. They were caused by the "rollers" which were little rubber wheels. The F80 design was plagued by it. Nikon eventually redesigned the takeup rollers and had a replacement part -- unfortunately after MANY trips to the dealer for cleaning and adjustment, I couldn't convince them and Nikon to step up to the plate and replace the faulty part. (No, it wasn't in warranty.)
So, I would immediately be suspicious of similar rollers.
The problem on the F-80 would sometimes go away for a roll or two after a cleaning. Seemed like the wheels would clog and stick from the slightest wear or dust. Try giving it a THOROUGH cleaning and blast from compressed air.
I have an MZ-M but have been lucky so far...
PS - Dollar Store film was GREAT for testing the scratching, removing processing from the equation completely. You can blast through a roll and rip it open without feeling guilty. If only the local dollar store would start stocking 35mm again....