Anyone installed a hot water coil in their HVAC ductwork to increase heat pump efficiency?
Better idea: flip things on their head

You need hot water to run a hydronic heating coil efficiently, far hotter than you'd ever set your water heater to (water heaters struggle to reach 180&deg;F which is the standard temp a hydronic boiler is set to).  However, your hydronic load probably pales in comparision to your domestic hot water load most of the time, and your current gas heater is not all that and a bag of chips regarding efficiency (EF=0.50).

So, the solution I propose is to use a hydronic boiler to drive an indirect hot water heater tank in addition to the coil in the air handler.  An indirect tank the size of your existing heater with a 150kbtu modulating-condensing boiler can give you practically infinite hot water, will have far fewer standby losses (~350-400Btu/hr for a Bradford White SW-2-80-L based on the AHRI figures of 0.6&deg;F/hr and a 71 gallon potable capacity) compared to the kBtu/hr range standby losses of a conventional gas heater, and will be more efficient than your existing heater overall with a computed EF in the 0.7 to 0.8 range depending on the thermal efficiency you can milk from the hydronic setup (good modcons get into 95-96% thermal efficiencies, and indirect tanks are quite efficient as well), comparable to a good condensing gas tank-type heater.

Atop that, you'll be running the coil in the air handler more efficiently due to the improved delta-T available over what a domestic hot water heater can produce, and you have a solid platform for future desires (such as zoned air handling or radiant heat).