Odd. As you are playing the internet expert and telling us the problem was unsolvable, I had assumed you knew all about this sort of thing. I mean, you wouldn't want to be exaggerating the level of knowledge backing up your assertions, now would you?

Anyway, consider: https://aip.scitation.org/doi/10.1063/1.4994054

This paper explains how one can storage power at an efficiency of 65-75% using machinery made with ordinary materials operated at modest temperatures.

That is a terrible efficiency.

It's acceptable as an efficiency for backing up renewables. The cheaper the input energy is, the less important efficiency is vs. the capital cost of the storage system.

Renewables are so cheap (and getting cheaper still) that you can pretty much just swallow the cost of the reduced efficiency.