Your tests seems conclusive but just to be sure, the scratches should be predictably in line across all frames and not scattered randomly.
I don't have the FE and can't verify by the manual I have but it seems removable as shown in MIR FE. In which case the obvious is a replacement pressure plate but probably the whole back which seems cheap and plentiful as it appears to share the same with all the other series FE, FM and FA except for the databack.