You could join the groups.io for more technical advice. There is a few repair guys there that know this model well. You can get lucky with info on this site to though. I have never done extensive disassembly on machines, but in cases of stuck grease in hard to reach places I have used oil to flush it out. I know these gears are suppose to be greased, but where there is no chance of mess or spill into motor or electrical parts it doesn't do any harm. The early 201 manuals with out potted motor call for oil on all three sets of meshing gears. Are you sure the turing parts near the bobbin case, race and hook on the 301 take grease? I have found detailed help on youtube tutorials, and if you are lucky,
this guy can give a few hints. You have to search up his full series on the 301 though. If you are very capable on the mechanical side you can go for more extensive work, but you probably get the same result with spray can oils, in stubbor cases flushing out with degreasers, but in most cases a light basic oil will clean out old dried up dirt and grease with repeated applications and wiping off. With a bit of frequent maintanance a machine like this usually cleans up flawlessly.