Electronic – Inverter VOH VOL

Yes, at this input voltage a center tapped primary with low side switches on the ends seems like the way to go. For feedback, I'd look at opto-isolators first. Put something on the output side that can detect whether the voltage is above or below the regulation threshold and drive the opto accordingly. On the primary side, a simple control method is to simply stop the oscillations when the opto signal indicates the output is high. If you can live with some ripple, this should be effective, simple, and efficient.

If you are considering connecting anything that might send power even accidentally into the mains network you want to be on your best electrical behaviour.

Generally what are used is two switches or contractors that are mechanically (and or electrically) interlocked so that your and the utility supply cannot ever connect to each other simultaneously. It prevents many dangers.

Check out the following picture search and see if something looks interesting. There will be DIY, off the shelf (OTS) and custom (PLC if you like) systems to do what you want.

https://www.google.com/search?q=automatic+mains+backup+relay&tbm=isch