I like insane hypotheticals that are discussed as hypocriticals. Not an engineer on paper, but these are my thoughts.
I think a very heavy weight that fits neatly inside of a protective structure with room to raise and lower it would be the way to get a kinetic battery. I’m talking about a platform stacked with concrete and rocks and sand and building demolition debris until it has stacked up to 2 or 3 stories tall. Then build a basic shell around it to blend into the town and have that 6 to 8 stories tall. The weight would tug at cables or press down on a hydraulic cylinder at a constant rate. A motor would then spin a large set of extreme reduction gears to raise the weight when there’s extra power coming in. Then, the tremendous weight could drive the reduction gears to spin the motor as a generator at a constant rate and make reliable power.
The less crazy version of this has been proposed, a set of cranes stacking up and lowering down more reasonably size blocks to store power inside of a tall structure.