You aren't touching the stovepipe in the top pic, heat transfer will suck. Don't use smaller tubing, you'll get more steam bubbles. Take the pipe you have, wrap it tight around a slightly smaller pipe, then force it over the bigger stovepipe so as much of it is in contact with the stovepipe as possible.
Alternately, cut a notch at the top and bottom of a section of stovepipe and put the coil inside the stovepipe. You'll need plenty of flow to prevent any steam bubbles.
The heat source should be below the hot tub as well so you always have the hottest water going up, not trying force it down after it's hot.