My point for the battery tender is, Why use the Coach converter/charger when you could use the battery tender? How much does it cost to repair/replace the charger portion of the converter? I can tell you, at Wal-Mart, a battery tender is $29.95, and lasts for quite some time.
Why not save the inverter for when you're on the road, and plugged in, or genset running, and really need it?
Just my thought. I've changed quite a few inverters and chargers. They're not cheap, at least at the RV dealerships I worked at.