I fully cleaned and reassembled the carb last night. The engine is still surging even though the float, needle and seat, and jet are clean as a whistle. I also removed the altitude adjustment screw and needle and cleaned it.
The motor now seems incredibly hard to start. It was a bit difficult to start before. Sometimes if I play with the kill switch by putting it in the "middle" position (between on and off) and pull the starter rope, it will act like it will start, then start after placing it back to the "on" position.
Could I have a bad kill switch? When it is hard starting it is getting fuel but acts like the plug isn't firing at all. Symptoms tend to get worse after the engine is warm which is one of the reasons I think the coil could be problematic.
I went ahead and ordered a new needle and seat for the carb just to rule that out since it is so cheap.