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.