Using battery power to go off the City's power grid

Make your own batteries. Easy.

My equipment was not happy with a consistent 123-125V I was getting for years, transformers humming, can't be good for transformers. I finally built bucking transformer to be rid of the constant humming.

I did suffer both microwave oven and furnace motor failures during this period of high voltage. Since utility finally came in and fixed over voltage issue, no failures, no humming. I monitor my voltage 24/7, now between 119-121V, exactly 120V at least 90% of time.

120V is the standard voltage. 125 is not even really high. That would be pretty common if you are the near end of a line run. Transformer hum is not from high voltage, it is from DC offset and sometimes from wickedly bad THD on the line. Likely there was an issue with the mains transformer and/or balancing on your line between phases causing a DC offset. Consumer electronics company (and motor, etc.) will do extensive reliability testing with low voltage, high voltage, etc. as field failures are very costly and easily prevented. A large DC offset if a much different beast. With transformers and motors there is nothing you can really do.

@theaudioamp I had forgotten about dc offset issue which I did know about at the time, this was many years ago when I had the issue.

You should realize that the power coming into your house qualifies as "perfect sine wave" yet it has (at my house) 4-5% THD.  

I am familiar with PS Audio power regenerators.  They analyze the power in with a scope and give you a THD reading for the incoming power.  

It would be extremely helpful if someone could power a PSA regenerator from some of the highly touted battery systems with "perfect sine wave" inverters and publish the actual THD numbers.  

Until then I'll remain skeptical.  Anyone who calls their power "perfect" is pretty much by definition lying.  But modern marketing practices allow it.

Jerry