Ok, so your using the electric tankless to provide supplemental heat when the tank runs cold, then. Here in California, electricity runs 35+ cents/kWh, so the relative cost is more dramatic. My local city is now outlawing gas appliances for new construction and 50%+ remodels, and they can have my natural gas tankless water heater when they can literally pry it out of my cold dead hands. I just finished my 90% remodel + 9% addition, so I'm well positioned that way.

Recirculation just keeps the HW pipes (and contents) warm, which should be insulated with foam. You can use a timer to decide when it runs. Gas heat in a tankless is pretty much instantaneous, but there is a "cold water sandwich" issue when there not enough mixing in the pipes.