You really shouldn't plan battery storage for winter/summer cycle. Batteries are for day/night cycle. If stretched a bit, then maybe batteries will cover "that

You really shouldn't plan battery storage for winter/summer cycle. Batteries are for day/night cycle. If stretched a bit, then maybe batteries will cover "that rainy day, when I need to do laundry" and similar. But not much more, as you've seen yourself - this is prohibitively expensive. For winter/summer cycle, if you're south of 40° N (and north of 40° S) just oversize PVs. Otherwise, you need a second power source - grid, wind or geothermal. Not to mention that having a second source is really good if you ever plan for maintenance or emergency repairs.