A 200' version makes 82%...

But that's pretty big. How about this?

We collect all the shower water in a tank, with an infinite cold water tank
next to it, then circulate the cold water through a coil in the shower tank
until it all cools to the cold water temp... Then again, infinite tanks are
hard to come by.

So maybe mix hot and cold fresh water to 90 F and circulate that through
the coil until the shower tank drops from 100 to 95, then pump some of
the 95 F fresh water back into the hot water tank and add enough cold fresh
water to make the fresh mix 85, then circulate for a while, then pump some
90 F fresh water back into the hot water tank and add enough cold water to
make the fresh mix 80, and so on. How can we do this automatically, on
a continuous basis? We need a 20 gallon expansion tank too. Lots of pumping,
but little energy, if the hot and cold supplies stay pressurized.

Nick