Thanks all for the replies and suggestions.
I ran 16 oz of Sea Foam through it mixed with a gallon of gas. I swear it even sounds better now. It no longer surges, or it recovers like it should anyway. When you first put a heavy load on it - like the AC compressor - it will surge about 3 times and then steady itself. Previously, it would hunt and surge continuously. That's magical stuff!
It was smokey though. I was afraid that it wasn't going to clear up, but apparently there was some left in the bowl after I switched back to feeding it from the tank. Without a load it used a gallon of fuel in about 1.5 hours. I'll have to keep that in mind when I calculate my fuel economy (every little bit helps).