Hmm. I looked at your site. You'll still run into some laws of thermodynamics. Extracting useful work from a temperature difference is always going to be less than 100% efficient.

And the cost of LN2 is almost entirely the cost of the energy to produce it.

If I had the money, time, and patience to build an energy storage system in my garage, I'd go with nickel-iron batteries. Your energy out / energy in is only about 40% but they last forever, have no moving parts, and are beautifully low-tech.

I thought a lot about batteries but they don't seem to provide the load response that a thermodynamic system can. LNG is also potentially a good choice but again with liquid nitrogen you don't care about the working fluid. Both work well for the major peak load problem air conditioning since the effectively replace that use case via cooling the air using a stored refrigerant. Current refrigerants are also a good possibility I'd say freon but it not freon any more. The problem with anything not liquid nitrogen is you have to store the gas till you compress again which is why I chose liquid nitrogen since you can exhaust to the atmosphere.