No-one has asked "why?".
If this is about a hobby and an electrical challenge then that's great and I am totally with you but if it is about saving money, then I don quite get it. Even if electricity consumption by the unit was equal between day and night, then you are only saving half the electricity consumption and spending a heap of cash to do so.
Electricity is expensive where I am but I'm pretty sure I couldn't justify the cost of your set up for a half saving on the running cost of a 150W appliance!
My main motivation isn't to save money, but even still, my return on investment (without worrying about replacing batteries) would be about 7 years, which is actually pretty good for any solar system. My primary motivation is to reduce my household dependence upon the reliability of the grid itself. An earlier poster cracked that my food would be spoiled by morning, not understanding the 'failover' feature of the plan, but that would actually be incorrect. So long as it's left alone & closed, and was well chilled about sundown, a typical well stocked fridge would make it to sunrise without going over 45 degrees inside a 70 degree home. The key there is keeping the doors shut, and plenty of already chilled thermal mass inside the fridge. Granted, it's not a good idea for your food to warm up above 40 degrees every night, but nothing is going to spoil at 45 degrees just once. I've experienced many power failures in my life, some of which only included my actual home, but the longest I've ever experienced was 4 days long. But I lived in the city, too. Now that I live in the country, most of my neighbors seem to think that my 4 day outage was short lived. That 4 days without power wasn't exactly hell, it was 72 degrees & sunny all week, but it would have been catastrophic if it had occurred in the middle of the winter. As it was, what we couldn't eat had to be tossed out by the second day as suspect. I lost at least $200 worth of food just that time. Since then, due to a just-our-house failure (actually, just a portion of the basement) I lost well over $200 just in frozen meat when our I found our deep freezer hadn't had power in an unknown number of days and was all thawed and room temps. I do have a genset that would run my fridge & deep freezer now, but I'd rather have a more permanent solution. And if I get it done by the end of the year, I can still get a 30% tax credit from my state up to $500. (So I don't want to go over $1500 total system, either)
For the winter power outage problem, I immediately installed an EPA certified woodstove upon moving to my, well wooded, country home on 13 acres. Much like the solar fridge plan, I wanted it to be something that I'd actually use regularly, and not just be a backup plan. My ROI for the woodstove & installation was only two seasons, because my fuel is free. Even so, I have actually used it as an outage heating system, because my propane fueled forced air furnace decided to die in the middle of winter. I know that I saved a couple hundred dollars in installation costs, simply by being willing an able to wait 6 days for a regular appointment, rather than drag a repairman out to the house at 10 pm on a Saturday night.
