I don't have any direct experience with Yamaha, other than staring at the kid's bikes that have taken up space in my garage, and little with two-stroke engines in general. Anything larger than a chainsaw here generally has a 4-stroke.

Most small engines in recent applications may have an "idle" speed but are expected to run "full throttle" any time they're being actually used. The governor can only regulate the "wide open speed" with any accuracy at all. The ones I've seen usually do use an "airflow" sensor of some sort for this regulation. With this kind of governor, some speed hunting is generally unavoidable at light loads, and many engines used in similar applications have virtually no "adjustability."

It's necessary to note that if you haven't RTFM - and believed what it tells you it will probably sound like an engine in this size range is running incredibly fast. It's meant to do that.

On most generators found here, the voltage should be regulated by controlling a field winding in the generator, and engine speed variations should not affect the voltage, by much if at all. Is it possible that the "service place" screwed around with the voltage regulator in addition to messing with the engine speed regulation?

If the generator has a fairly good voltage regulator, properly adjusted, engine speed variations should be "tolerable," although you'll need specific information for your set to assess whether something really needs to be fixed. Engine speed variation may cause a frequency variation, if it's a simple system, but that's not usually considered objectionable in small units of this kind. (Just don't try to run your clock off it.) Light bulbs and motored appliances don't really care much about incredibly accurate frequencies, and everything in most "electronics" is "DC inside" which isolates the innards from outside frequency hunting.

If something really is out of spec, you're best bet is to check with the generator set manufacturer for a maintenance (and or rebuild) manual for the generator set.

(They may have a FAQ where you can find some info, but most FAQ sites rely on the ability of someone to ask an intelligent question and that seldom happens.)

You'll probably also need to separately look for maintenance/service/rebuild manuals from the engine manufacturer. My Briggs and Stratton manual was about $35(US) a couple of years ago, and covers essentially all engines they've made in this century, so if you get a similar one from Yama maybe you can set up your own shop and make enough to buy few rounds.

An option: for a tiny unit like this, if it has a DC output, is to use the generator to charge a battery and get yourself a 500W solid state inverter for AC power. The battery will take care of voltage regulation, and a "fair" quality inverter should give you good enough frequency control. My 500W inverter was about $70(US), although it might be a bit more with the higher voltages in your place.

John