I think you're doing something wrong here. Either your math is bad, or you have the world's largest water heater that's about a mile from your house.
I don't remember the last time I saw a 120VAC water heater; they aren't exactly common.
6 awg is used for electric stoves @ 50amp, which is more than you describe.
6 awg is also used for water heaters (240vac @50amp)
8 awg is used for 240vac clothes driers @ 30amp
My water heater has dual 5500w elements, which consume just shy of 50amp, and that's the biggest one they sell at the big box store.
Also remember that a 120VAC appliance does not need exactly 120VAC. Fluctuations at your local neighborhood transformer can drop that as low as 110VAC.
In a normal-sized house, you don't generally need to worry about voltage drop on a/c lines. For example, in my house, my line voltage is 120VAC in order to compensate for any possible drop on-premise. My shed has an underground run 300' from the house and measures at 110VAC, which is perfect.
Edit -- now I understand the problem more completely. Instead of putting the 20 amp breaker in your panel, put a 50 amp in there and run a daughter box at the remote site with a separate 20amp breaker. RV panels are great for this [http://www.menards.com/main/electrical/circuit-protection-distribution/rv-panels/120-240-volt-20-amp-gfci-rv-power-outlet-plus-50-amp-with-breakers/p-1444427371346-c-6440.htm?tid=8800702129165764672]
- You get 50 amps at the remote site! Plug in a welder too!
- A 50 amp breaker takes a 4awg wire just fine
- No splices in the panel
- No voltage drop