That sounds logical, but could you explain how I recirculate the water through the tank? Is it a recirculating pump or are you talking about a way of rerouting the water through the water heater? I’m just trying to picture it...
I have a flat plate. The DHW side is T'd into the DHW tank at the bottom feed inlet, and the top pressure relief port. I have a little circ pump that circulates that side, with a Johnson A419 temp control controlling that. But, if you are only wanting to heat DHW when you have your wood boiler running & flowing, using a sidearm HX plumbed in the same way would heat your tank up by simple convection on the DHW side - without a pump or controls. I started out that way, but it wouldn't work very well when I wasn't burning for heat and just burning for DHW by heating DHW from my storage tanks. I could only go 3-4 days between fires. So I added a flat plate to the circuit and got to 7 days between fires. After all that, I don't heat my DHW with wood in the non-heating months anymore, unless I have some stuff to get rid of & it's a chilly day & I decide to make a fire on. So the first sidearm setup I had would do the job for me now. When doing any of this, you should also plumb in a mixing valve after the hot water tank outlet so the hot coming out of the taps won't burn anybody - the tank can heat up pretty hot if you are burning away and not using any DHW for quite a while. Unless you control the flow to the boiler side of the HX with a zone valve - but that won't work if your boiler loop is all one long series loop. Such as a lot of OWB setups are. The tank could heat up enough to trip the overheat stat on your heater - something else to keep in mind. I think mine trips when the tank gets to the 160 area. Which doesn't happen any more since I went to the controlled circ & flat plate.