Use of a 10w50 instead of an Xw20 is going to make a much bigger difference as fuel economy goes in your usage than in more typical usage. When you're idling and the only loads are the AC and electric the engine is already in a very inefficient operating mode. It's fuel usage per hour is lower than for a car that's actually driving around, but pumping losses account for a huge percentage of energy use. Because of this an Xw20 makes that much more sense from a fuel economy standpoint.
A thick Xw30 or thin Xw40 is about the thickest that could make much of any sense in that scenario and is understandable if you're nervous about high heat, perhaps in the event something goes wrong. For a little extra feeling of safety, maybe you want to choose a synthetic Xw20 with a high VI so it doesn't thin out as much if it does somehow get extra hot, but still get the fuel economy advantage of an Xw20.
One way or another, that is a car that should be very reliable and it'll be in a usage scenario that is very easy on both the engine and the oil. If you're really concerned about having a safety net, how about keeping a sort of a emergency kit in the trunk:
-5 gallons of drinking water (in case something really bad happens)
-2 quarts of name brand synthetic 5w30
-2 quarts of 15w40 in case you manage to spring a leak
-a gallon of undiluted anti-freeze (can also be used in brake system in a pinch) and some ground black pepper
-a gallon of Everclear or similar in a metal can as emergency fuel supply/disinfectant
-an oil filter and tools for both the filter and drain bolt
-a couple of rags and a pair of dish washing gloves
-a solar powered trickle charger
-a small toolkit with a ratchet and metric sockets, screwdriver, hammer, and pliers
-a tire plug kit and 12V electric tire inflator with work light
-a roll of gaffer's tape
-some zip ties
-a plastic tote to store the fluids in so no worries about leaky bottles
-a few feet of bailing wire (oops that boulder broke my tie rod)
-a roll of aluminum foil (always good to have)
-a length of nylon rope (see aluminum foil)
-a plastic tote for all the fluids except the water, just in case the bottles leak
Addition:
Maybe the emergency kit could also include two short 12 gauge shotguns and 50 shells in a proper ammo box just in case the Zombie Revolution starts while you're on the road.