So, I pulled the carb off the bike today and I think I made some headway.
Here's the pilot screw being almost all the way in. Adjusted it out to 2.5 turns, it doesn't smell any richer when I went on a quick ride, but I'll check the plug later after I get some more riding in.
Here's the float needle, I pulled it out to make sure it wasn't worn or damaged. Didn't look too bad.
Here's the jets inside. PO really did a number on the float pin screw. Go figure. Anyway, I pulled all the jets and cleaned them. I was talking with my father and he suggested that I check and make sure that the float actually worked properly. I dropped it in float bowl full of gas and it floated fine at first and then one side sank a little bit. So I'm thinking that the float might be at least partially responsible for all the gas consumption issue. Although, I did forget to check to see if it was just a float adjustment issue, so I'm going to check that a little bit later as well.