First off, your genset is pretty close but it should be closer.
Generator output frequency is a function of generator speed. I am not familiar with the MDKC but I do have a 15kW MDJF. On my unit, there is an adjustment screw under the platform that holds the water
pump. This screw is unique. There are machine threads in the platform and very prominent Acme type threads with a spring that rides inside them. The spring controls the governor, as I recall
To adjust, monitor
the line frequency and adjust the no load frequency to about 62 Hz. Load the generator while monitoring the line frequency and observe its reduction as the genset loads up. This reduction is known as "droop". More modern gensets have a droop adjustment. Adjust the genset speed so that it produces 60Hz @ 80% of genset rated capacity and you should be ok. If you have a droop adjustment, you should be able to get spot on.