The concept of flywheel storage for the grid has been around for several decades. Some years back there was a consideration of flywheels about 200 m in diameter. One proposal was to make them of bamboo fiber.
The rotating energy in the grid even now is several minutes worth of operation, due to all the dynamos on line, plus some number of synchronous motors doing phase correction.
My best guess is that the axes of the big ones would have to be oriented parallel to Earth's axis to keep them from climbing out of the ground. I'd put them in deep pits.
Levitation by using magnets working against superconducting bearings might work. The levitation works by excluding the magnetic field. This can be made stable ... its the principle behind maglev trains.
I think the technology is workable with conventional bearings and synthetic lubricants.
This project, though, is tiny, the size of a football. I don't see precession as an issue ... just gimbal the whole thing. One of the problems with previous automotive flywheel concepts, which were maybe 1.5 meters in diameter, was that there was no way to rigidly mount a flywheel of that size that would not result in bizarre precession characteristics, like doing a wheelie when you crested a hill.