Ok, I made a lot of progress. Took most of the carb apart and cleaned it. Notes:
significant dirt on screen
the diaphragm seems loose to me (does seat well)
dirt behind the main jet
I reset the brass mix screw to 2 turns out. I was significantly more than that.
Right now, I'm debating which parts I'm going to replace. I'm on a budget, but don't want to regret not doing the job right and having the same problem after I reassemble.