RE Voltage drop

This is why buildings are wired with AC at higher voltages. We are use to Ohms law but forget Watts law, a derivative of Ohms law. In essence it means the higher the voltage, the less the current that is requred to accoplish the same amount of work. wattage is figured as voltage times current. So if the load draw 100 watts you need so supply 100volts time 1amp, or 10 volts times ten amps. When we say we have a voltage drop on a length of wire ( for the other readers who do not know), it means that there is a current loss through the wire. The hevier the wire is the less loss there will be.
Now the example of 100 volts vs 10 volts that I gave isnt quite that simple as the equipment you are using must be able to use they voltage source you have. In the instance of our House wiring being AC at lower current levels, all the equipment we use is designed around that source. But when wiring a house for DC the fact is there is no real safe wire size, due to heating dependent on the load. Realistically 0ga is about the only safe minimum diameter to minimize fire hazard. AC however does not have this issue as long as the wire is not coiled up. Not going into the math or long explanations the average voltage of a 120 volt AC line in the wall is zero volts (sine wave crosses zero voltage remember?) so this limits heating under load, but DC under load just continues to generate heat, even on good conductors when under load unless the conductor is massive.

OK all the background is in place, you have the right idea but implementation needs modification. Dual batteries outside, raised off the ground. with binding post connectors on insulated plates mounted on a junction box in the room with a gennie type twist lock plug junction box outside with mated plug and cable to the parallel wired batteries. To this add a solar panel and controller (check out harbor freight under 200 bucks) and this should do what you need. Also avoid the myth of the Golf cart batteries they are made to be recharged and discharged a lot but do not have the deep cycle capacity, and if drained down til dead and recharged too often they will be destroyed. they are not made for deep cycle use. I hope I didnt go overboard on explanation on the whys, not knowing expertice levels here yet, the background info helps make the rest of the info useable in other endeavors