@Donald Qualls An engineering/efficiency geek in me instantly activated upon seeing your message!
Some rough calculations: heating 5L of water by 18C takes about 90kcal or just about 0.1Kw/h. This is about $0.017, taking the average energy cost in the USA. That's what you're optimizing: for the most efficient way to spend less than 2 cents.
I would argue that your central heater is more efficient than sous vide because it may be using a cheaper energy source (gas in many states) and it is insulated. Meanwhile, a sous vide will be fighting the temperature loss due to ambient and driving the pump. I also don't see how any water is wasted? It's trivial to fill up the tub with water of desired temperature, and it will be well-mixed too. Just open the hot faucet and start filling up the tub. Eventually it will get hotter, then you open the cold faucet, and you're done. Not a single drop of wasted water. After a while you won't even need the thermometer, because 110-115F feels just slightly warm and you don't have to be precise.