Here is what I would do, eliminate the possible electrical issues first. Bypass the oil level sensor by looping the wire or breaking the connection(which ever way it works). Next get yourself a 5 dollar inline spark tester, start the engine and run it, do you see the tester flashing consistently or does the light miss once it warms up? You can also try putting a hair dryer to the cdi box before you start it up to see if it acts strange right away. If those check out, next you will need to get a can of starting fluid, with the air cleaner off you need to meter starting fluid through the carb throat when it starts to act funny, if you can get it to smooth out than you have a carb issue. Unfortunately since it is a POS California carb you will probably not be able to make any adjustments to the fuel mixture screw or other adjusters. You will need to remove the carb from the motor, remove the bowl and jets out of the carb. You are going to need to make sure that the orifices are clear in each jet. Next you need a compressor to be able to blow out each orifice in the carb and ensure that air comes out of the respected exits of each orifice. Every orifice has an exit somewhere, make sure that each hole you put the compressed air to exits somewhere else on the carb. One more thing, you should disconnect the governor and run the governor yourself to ensure that the governor isn't just acting funny and killing the engine. After you have done these, report back.