Yes, you are on the right track, as the other suggestions, always do the cheapest, most likely items first, and injectors are right up there for poor combustion leading to oily sheen. If you have good injectors, next item to check is the delivery valve(s) of the injection pump. Another item for poor combustion common in gen sets is running at low loads, and long runs at low loads (under 70-80%, so 34 amps on a 6kw gen set rated at 40 amps) because you make carbon that builds up in the exhaust ports, restricting air flow, making the mixture fuel rich therefor oil sheen. Pulling and cleaning the exhaust manifold (and avoiding low load running) is also an easy check to solve the sheen.
best of luck!