There is an Immersion Heater M-67 used by the military that should work perfectly for your use. Will run on almost any fuel that burns including old engine oil, diesel, kerosene, gasoline. They are still available surplus new and generally sell for around $100. US. A great idea over reinventing the wheel. Of course it isn't a rocket stove but the payoff is using discarded burnables.
For me spiraling isn't the correct method. You can use straight pipes with u-turns or 2 x 90 degrees turns. You can also easily replace damaged pipes which is not the case for spiraling. You can place straight pipes vertically or horizontal, water always find a way.
The best way I can think of is to fill your tub with cold water, and have the tub up high, have the rocket stove barrel up against the bottom of the tub, heating the water by heating the metal tub from below. A cast iron tub wood work the best. Be sure to place a wooden rack in the tub so that you don't scorch your butt. I know people who have done this with a fire under the tub. Same principal.
"Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has."-Margaret Mead "The only thing worse than being blind, is having sight but no vision."-Helen Keller