You might try these tips.
First connect your freq meter to as utility source and see that it reads 60 Hertz correctly.
Then set the gen speed at 64hz no-load AFTER you have done the STATIC governor adjust. Voltage may read 135 volts but less than 140.
Connect the governor sensitivity spring in the notches or holes that has the spring at it's greatest tension. make sure that Bubba has not installed a weaker or wrong spring. This spring must be strong enough that the governor will pull the engine speed up and keep the engine governor from hunting up and down between load and no load. (that is why is called the governor sensitivity spring when used on a gen) Each time the spring is in a different notch or hole the no load speed will usually require a slight tweak adjustment for 64 hz.
Start the gen and set the no load speed at 64hz with no load. Also turn in the carb
idle adjust screw as far as it will go so as the low engine idle is held at 64hz, get a longer idle screw if necessary to accomplish this.
If you add and removed a 2kw load and the engine speed hunts up and down quite a bit before it settles most likely the governor sensitivity spring is weak or the governor mechanical linkage is sloppy. I've made temp repairs to weak springs and also added another spring either over or inside the existing spring. (quite common for the springs to become weak and a hint is the engine will hunt up and down quite a bit between load and no load) On Coleman gens this spring is the one connected to the no load engine speed adjust arm.
You can reduce the amount of up and down hunting on gens that do not have the low idle function by using a long low idle screw to hold the engine speed up a much as possible
on constant rpms gens with a weak or sloppy governorThe engine when using the longer low idle screw don't have to recover as much from the dip in rpm as the load is first applied. Also slightly tweak the high speed carb adjust while the engine is loaded for max rpms if the carb has a H jet adjust. sometimes just a 1/8 turn on a warm engine is enough to not get good engine load response if the H jet was adjusted a no load or when the engine was cold.