Gyro energy density is defined only by tip speed. And that is limited by material strength to weight ratio.
Why not use ultra high density polyethylene (Spectra / Dyneema) for gyro disks? It has a very good strength to weight ratio and is composed of just hydrogen and carbon. I imagine using modern manufacturing techniques (which you have to use anyway for this material) you could get very accurately balanced disks straight out of the process.
To get to lithium ion energy density category, we’re talking about 1 km/s territory, supercapacitors 200 m/s.
Formula one is introducing brake energy recovery, and some teams are using gyros instead of batteries