If you haven't got one, get an Oxygenics shower head. They use a lot less water.
A 2nd HWT would have to be a lot of work and expense. The recirc. line sounds interesting.
I would consider the recirc. method but if you remove the underbelly material, I would use a recirc. pump and line like they do in commercial buildings. They draw water from the HWT and recirc. it back to the tank's cold water inlet so you have instant hot water. You'd need a pump that could handle the temp. like a solar hot water pump. You could mount a switch somewhere so you would turn it on only when needed. A rotary timer switch would also work.
A recirculation pump would be a lot less work and $$ and would not add much weight in comparison to a 2nd HWT.
While you have the underbelly material off, I would replace the OEM tank sensor probes with Horst Miracle probes.