Yeah, it seems to me that placing the copper tubing directly inside the burn tunnel, heat-riser, or heat-exchange-barrel ... placing it directly inside any of that is way too extreme.
I don't know, you might even melt the copper? Yeah, actually you might: the melting point of copper is just
under 2000 degrees Farenheit, and in the book ,Rocket Mass Heaters, by Ianto Evans and Leslie Jackson, the interior of the combustion unit can get up to 2000 degrees Farenheit. (see page 59)
Also, partially exposing the heat-exchange barrel to the water sounds extreme. An interesting EXPERIMENT, but also EXTREME and potentially blindingly steamy hot-death-to-your-eyeballs when the hot tub leaks or splashes and hits that extremely hot steel. Another thing is that the heat-exchange barrel is intended to exchange heat with the air, submerging it in water may affect the temperatures and the internal burn-processes: colder burn, less clean, less efficient.
You may want to check out this podcast:
http://www.richsoil.com/permaculture/613-pocast-098-hot-water/
Also, definitely, this (not just about floor heating, but also water heating-- check out the 4th picture down):
https://permies.com/forums/posts/list/40/5937