I was able to coax the forge into drafting by cheating. I used an in-line duct fan at the far end of the chimney. 25 feet was enough ducting to dump enough heat to keep the fan under 140 degrees.
I didn't cut the video, so it's stupidly long…
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If you use a "Y" piece of ducting flipped upside down and placed the fan ,with it blowing into the duct, on one of the legs of the "Y" the other leg of the "Y" will be your exhaust intake and the top leg of the "Y" will be your exhaust. You will achieve two things. One you will be pulling cool air across the fan and two you will be pushing the air which is more efficient.