I understand gravitation isn't the only force... how are you proposing to store energy? Other options (beside pumped hydro as gravitational potential energy storage) that come to mind are flywheels, springs, or batteries .... all of these technologies have existed for more than 100 years, and batteries are the only ones currently growing in usage - there's a good reason for that.
Batteries are being used primarily in electric vehicles, for, as you say, good reasons, and for domestic backup. For bulk utility storage, batteries are the most expensive choice, although battery cost is still falling fast and numerous utility-adapted chemistries are competing.
F may be water pressure, as in pumped hydro (which is growing) using elevated or underground reservoirs, or air pressure, as in CAES underground or underwater compressed air, or buoyancy using sea-floor pulleys and floats. No doubt as a soon-to-be Licensed Professional Engineer you will soon be able to think of other persistent forces.
Springs and flywheels will not be used for bulk utility-scale storage.
Generally, utilities will use what is cheap and reliable at the time they build it. Building storage before you have enough spare renewable capacity to charge it would be a bad misallocation of capital
Anhydrous ammonia will not be the cheapest medium, but has advantages of transportability and fantastic usefulness. Any unused overbuilt capacity will be put to work synthesizing for sale.
