I am posting this to close out the thread and hopefully help someone else with these issues. Before breaking the carb apart I decided to change the spark plug which resolved the issue of the kart dying after a few laps. After changing the spark plug the apparent rich condition was also eliminated once the engine was brought up to temp (110 degrees). As a side note, I also added an additional breather tube to my gas tank cap using a 1/4 inch copper barb which eliminated a bogging issue I was having when I had more than a half tank of gas and I would come off the gas and try to get back on it.
To summarize, here’s the issues I had and the things that fixed them: