One other thing important in cold start cranking is the choke. If you take off your air filter, when you've done everything (switched the key on and/or floored the gas pedal once) to set the choke and are about to turn the switch to "ignition," you should find that oval choke butterfly on top of the carb closed, meaning flat. The choke can be adjusted, but it should start in closed position. The earlier symptoms you described are probably not choke related, but sheer cranking could be that.
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