We have a tankless natural gas hot water heater. When you go into a bathroom and turn on the light switch I have the water start circulating so by the time you need to use the hot water it is there or very close.
Our kitchen switch light does the same thing. This almost eliminates the sandwich.
http://ecorenovator.org/forum/renova...er-heater.html
I had a tankless feeding a 40 gallon natural gas tank before similar to what you are asking about. (Except the HP part)
The new setup works better than the old one for less energy usage and faster hot water at the sink. The equipment was less money also but not cheap.
we have endless hot water.
Last month usage was 4 therms $12.49 this is a family of 4 with one teenager.