>Perhaps consider running a recirculating line back for your hot water demand since you have all the tools and access points open.<
This is common in showers where the HW is heated with a gas unit.
Turning the water off -on requires the heater to stop , then play catch up so the water temp varies.
The simple solution is to install a tub/shower control and simply plumb the tub back to the FW tank.
May cost a bit of energy , but not a drop of water.
For a power hose boat , the Euro system of returning some tap hot water to the tank via a heating towel rack is first class.