Get a multimeter that reads Frequency. Start the set, run at idle. Measure frequency at the 110 outlet. Monitor the meter while slowly increasing the Hertz. Does it really go up? If so, how far.
Normally, if the gen set overspeeds, the idiot light comes on, and then shuts the set off. At this point, the gen set should not allow you to restart the set. That's the reason for the S-10, (Overspeed switch) reset. Yours allowed you to restart the set, without resetting the S-10. Sooooooooooo, it's also possible that your speed switch has a set of contacts that hang up. Is the speed switch a mechanical, or electrical type. The mechanical type is the old, (old, old old!) type.
Partner, you need to download the manuals and troubleshoot the freq problem first. The TM tells you what the output voltage is for the frequency transducer is. The input of the freq transducer should be 110 volts, more or less. So check that, and compare.
Also, forgot to ask. Did this gen set ever work right? Or did you just get it?