One thing you might need to do is clean out the pilot jets. These are the smallest jets in the carb. Sometimes they are plugged up from years of buildup, sometimes it's just a spec of sand/dirt. If you haven't done this, it might be part of your issue. Also, the same applies to the main jets.
Here's a video of a Vanguard carb. It's different from what you have, but for informational purposes it will let you see how these things work.
https://www.youtube.com/watch?v=xOliwvhFsY0
Removal of the pilot jets is tricky. You have to make sure you use the correct screwdriver or you'll strip out the head. You want the largest slotted screwdriver that will fit into the slot.