Start with checking the points condition and gap. Check the distributor shaft for side play. It needs to have minimal movement, any wear and the points will not stay set. That can cause strange things, loss of spark at various RPM and temperatures.
Check the spark quality at the plug end of each wire. It should give a 1/4" blue hot spark to ground.
Pull the drain plug in the bottom of the carb bowl with the fuel valve open, engine off. be ready to catch the flow in a clean glass. It should give a full flow, not stop flowing or slow to a drip. If it doesn't have good flow, check the screen in the carb inlet fitting, the sediment bowl, and inside the tank. Be sure the cap is vented. Try loosening the cap even if it says vented, it may be clogged. If there is an inline filter, that may be part of the problem. They don't work well with gravity systems.
Look at what was caught in the glass. If water on the bottom, or trash and rust came out, the tank is contaminated, and the same will be in the carb, even though it was recently cleaned. The tank will need to come off and be cleaned, and the carb may need to be eased apart and cleaned out.
As for the governor, engine off, dash lever at fast, look at the throttle shaft on the carb. It should be spring loaded to the full open position. Then with the dash lever in the idle position, the throttle should be held closed against the idle stop.
If that is not happening, there is a problem with the governor linkage adjustment. Let us know and we can walk you through the adjustment.