The speed variations you described sound like "hunting" - this is something governors do, nearly always because the mixture is too lean. What happens is that the engine cannot hold the speed the governor is calling for, and gradually slows down. When the speed error becomes large the governor slams the throttle open, which triggers acceleration enrichment, allowing the engine to carry the load and speed up to the governor setting. However as soon as it reaches the set speed, the throttle partly closes, the mixture goes lean again, and the speed sags again.
The cause of lean mixture with 2 strokes that have non-adjustable carburetors is nearly always an air leak into the intake pipe or crankcase, low fuel level in the float bowl, or an obstructed main jet. In this case you may have leaky crankshaft seals, which allows air to be sucked into the crankcase. This air has not passed through the carburetor, and therefore has no fuel mixed with it. This results in all of the mixture that goes into the cylinder being leaner than it should be.
