And disclaimer: no one should do this, but when the transfer switch disconnects from the grid, would it work to jump say a breaker across the L1-L2 hots to share that 120v backfeed over both?
Clearly the 240v appliances won't work in this configuration, but the fridge on one leg and the internet on the other will still work ok, right?
Again, no one try this - it's just a thought exercise.