I'm not sure which question I am answering but, YES on the main jet.
The speeding up you talk about could easily be a lack of fuel flow and running out of gas is a sure way to stir up any available crud.
Make sure you have good gas flow with the gas line disconnected, you can disconnect the banjo at the carb. There is a filter screen inside the tank around the pet cock. Also, look inside the Bolt which holds the banjo to carb, Mine has a small screen in there which can reduce fuel flow.
After that, you are left with the main jet mostly. Make sure you separate the jet from the jet holder to clean and examine it.
All of the above can be done without rermoving the carb although you should check that it is seated all the way onto the manifold.