It looks like you did this the hard way.
Back in the seventies I was a on site manager of a small apartment complex that had a centralized hot water supply. It had a 80 gallon tank for 10 apartments!
They designed the system with a simple recirculation pump. It consisted of a return hot water line from the furthest tap back to the hot water tank. The recirculating pump was in the return line next to the tank. There was no pressure change as the pump moved only hot water through the pipes. In the case of the apartments it added about 200' of 3/4" pipe to add volume.
The pump would run constantly to provide hot water through out the system. In your example you would want to put an on/off switch on the pump to access the "instant" hot water and with it off it would work as if the pump was not there!
Only issue I can see is that the return line needs to go directly into the HW tank, so that the cool return water would cool the HW causing it to reheat. (Edit) Just thinking this through, you could put a'T' in the cold water line just as it enters the HW tank.
Only parts needed:
2 tees
1 recirculating pump
Length of hot water pipe/tube
1 on/off 12v switch
