Saw this last week, really enjoyed the tenacity in problem-solving!!
Did make me wonder if you could build a solid state one using well-timed pulses through an electromagnet that provide torque through the field interaction with the earth's magnetic field.
Not much torque available there obviously, but on a per-revolution basis you don't need much.
The physics of magnetic torquing maybe could probably work in most if not all locations on Earth for a sufficiently small and power dense vertical top that spins sufficiently slow. Want the smallest possible local dot product of gravity vector and magnetic field for an ordinary top (without considering "sideways" tops), which may lead to better performance in some locations on Earth (could map this with e.g. IGRF). 3D field actuation would be beneficial to allow higher efficiency and longer periods of actuation around the window where the Earth's magnetic field is maximized in the spun plane, while minimizing imbalance: this actuation timing is probably the only strategy that would make practical sense for most of the magnetic power, because you will need to take a break once in a while for sensing. Another practically difficult part would be avoiding on-board soft iron noise in magnetic field, because higher spin speed would require the device and environment to damp out the device-induced magnetic field at a higher minimum rate to afford any budget for accurate sensing of the background field during the "off"-time. That is: sensing trades with spin speed because it takes non-zero time and requires a stable environment.
To implement this, I think you'd first want to test in a controlled environment with a larger magnetic field and then gradually turn down the applied field until it is Earth-like. I am honestly unsure whether you could practically get there, so earlier I used the words "maybe could", but humans are crazy so I appended the "probably".
Did make me wonder if you could build a solid state one using well-timed pulses through an electromagnet that provide torque through the field interaction with the earth's magnetic field.
Not much torque available there obviously, but on a per-revolution basis you don't need much.