An alternative to Mouse Milk additives is to change the oil to a diesel grade like Delo 400, or Rotella T.
15W/40 grade.
CD grade diesel lube oil has to effectively deal with carbon. The oil's additive package removes carbon many times stronger than what your rings are dealing with. The oil temp should reach 190 degrees and stay there for several hours. The most effective treatment is to run the generator loaded for an hour or so, wait a week and do it again. The repeated soak of CD oil into the ring lands will remove gum.
There is no way CD oil can hurt the engine. Like giving the gummed up rings a dose of the salts. Unless the rings managed to get broken this is an effective treatment