A complicated algorithm for the relays evolved to where they're directly toggled on & off by the power button.  They connect the inverter for voltages below 11.  They connect manes for 11.  10 sets the maximum inverter voltage, which could be higher than manes, but could also be battery powered.  They wait a while in the off state when switching between relay & manes.  They always switch off with no delay.  The delay avoids back EMF & the chance of a timing glitch briefly connecting manes to the inverter output.

Of course, the very thought of that timing glitch & the chance of a relay getting stuck has lions pondering not allowing a manes bypass at all.  The piece of mind might be worth the lost efficiency.  It needs to sense the outlet is off before powering the inverter.

The relays suck a hideous amount of current, 75mA for each one that's on.

Putting it all together requires mounting everything on the enclosure base plate.