That Sakura heater would probably work for you. It would literally produce steam from the tap.

When I got it, I assumed that using all hot water and regulating the heat at the heater would be most efficient, but that required running the heater at about 75%. Later I found that the slower the water flow, the hotter the water would get, so I could run the heater at about 30% and mix in cold at the shower for the same temperature. That Sakura didn't have much in the way of fancy control, just a big knob for flame (like a stove), and some basic sensors to keep it from overheating or turning on if there was no flow. Steam in the hot water pipe it was OK with.

The new Rinnai won't heat the water over 140°f, limited by the software, so you can't burn yourself. As a result, now I do use just hot and regulate it at the heater control. It is set up such that you can parallel up to 4 heaters on one control. It uses more gas than did the Sakura, but it's easier to live with.

You're right, a second heater in the bathroom would be excessive, which is why I haven't done it, but it doesn't stop me from wanting to...