One deep cycle battery doesn't last long. And damage occurs after going below 50% charge. I have my solar panels connected to the best charge controller you can get (Midnight Classic), and I have 4 high quality (US battery) 12 volt deep cycle batteries. It doesn't last as long as you might think. The problem is the 123 volt system. There is a lot of loss going from 12 volt to 120 in the inverter. The loss is nearly 10:1 (12x10=120 volts).

That being said, I can run my freezer, fridge and some lights and have several plugs in my house wired to the inverter. As long as the sun shines I'm OK, and even then I have to use aggressive power management.

A better solution for lights are rechargeable LED camp lanterns that you charge off your inverter.

I knew a guy that had more panels than me and 16 deep cycle batteries. Even with the sun out, his battery bank was dead in a few days. His mistake was wiring the inverter through his panel to power the entire house (except air conditioning)

But, keep up the good work. You're a long ways ahead of most. You're thinking.