Prototype: 12 DC car battery to power standard 120 VAC hand tools
I think your math all checks out and you have good command of the concepts here.
You need a few more concepts though.
Lead-acid batteries are bizarre. While they are cheap, they do not work the way they obviously ought to work.  The #1 thing they don't do is deep-discharge well.  If you run a lead-acid battery from 90% to 10%, you will get three to 100 of these full cycles before the battery loses capacity dramatically and is kaput.
People who depend on lead-acid batteries for deep-cycling find they can only use the top 30% of capacity on a regular basis or they will get very short life out of their battery.
Further, the type of battery matters a great deal. Car starting batteries are made for delivering a big one-shot impulse, but do particularly badly in deep-cycling.  Deep-cycle batteries do well with deep cycling, but have too much internal resistance to start an engine in adverse conditions.
They are a big pain in the butt, but you like the price.
If you want a battery that actually behaves like it says on the tin, then look at lithium (which has different kinds of feisty) - or the perfect large battery is nickel-cadmium or nickel-iron.  I have a set of NiCds that came to us as scrap in 1986, and they're still going.  Nickel-iron is impervious to almost any operational abuse, and last 40 years, but have quite high internal resistance so are not good at starting engines.