We are in KC and our backyard coop has no electricity. It's close to the same size as yours with no run. What we did was pick large birds that are winter hardy (Orpington and considered Jersey Giants but didn't have a local source). I don't think running juice to the coop for heat is necessary, even in your situation. Maybe your coop can be insulated, and designed with functional shutters on the windows? Maybe designed with eye hooks on the exterior corners, so with exception of the access door, it can be wrapped in moving blankets topped with tarps to water proof it in the winter, secured with bungee cords? I'm picturing the wrap being similar to the insulation around a home dishwasher. Not pretty but it could keep your girls protected from the wind.
Daily 'chicken chores' here are done 2 times a day, morning and evening, which consists of scooping solid poo from the pine shavings on the coop floor and putting into the compost. We treat it similar to cat litter and actually use a litter scoop. Then as needed we add more shavings to maintain bedding level at 4-6 inches deep. We haven't had a bad odor issue at all, and have yet to completely remove the bedding and replace it after about 2 months. It seems to disintegrate to dust as the birds scratch around in it. We even left town for the weekend and didn't ask the pet sitters to do anything with the bedding, and it wasn't bad when we returned.
3 times a day we make sure they have fresh water. We use an anti-tip dog food bowl for food, since they love standing in it, and tipped over all the other feeders. I'd put daily maintenance at 10-15 minutes tops. If you want tame birds that aren't skittish around people, that will take a little extra time, but will be worth it especially if you have skeptics in the group.
Maybe you can build the coop to have its own rain barrel, if the roof can handle the weight? Wonder if it would be safe to water the chickens from that? Possibly hooked into an automatic waterer? Hauling water would not be fun!