As Avgas is 12Kwh/kg but engines are only 25% efficient then it means only 3kgwh/kg is used, as electric motors are 85% then any battery about 4kwh/kg or over is about the same as Avgas.
I don't think your numbers are realistic. My 1966 aircraft delivers 150 kW on 50 litres of 100LL per hour. That's about 4.2 kWh/kg. So you're in the right ballpark, but being a bit optimistic.
nanowire batteries that have just been patented
That should ring alarm bells. I think 5 kWh/kg batteries are a very long way away, I'm afraid.