So... I think you are close, perhaps you are a bigger picture person and so have missed some details...
Leave hot water tank bypass in bypass configuration.
Partially fill fresh tank and dump a couple of times.
Fully fill fresh tank and ad a cup or 2 of unscented bleach.
Turn on water pump and pump mixture through all lines till pink stops pumping out.
Drink a beer.
Drain fresh tank.
Drink another beer while tank drains.
Fill fresh tank and pump through lines till bleachy water is gone.
Turn off pump
Remove hot water tank plug
Reconfigure hot water tank bypass for in line use.
Turn on pump and allow a small amount of water to escape the hit water tank, I will often open a near by hot water tap and insert the plug allowing a portion of the tank to fill and remove the plug to be sure any bugs are rinsed out.
Turn off near by hot water tap, turn of pump lube (food grade lube) and reinsert the anode rod in the tank.
Turn on pump and allow tank to fill.
Test all systems.
Done.