The stainless steel flywheels though..... No ideas.
Or maybe a pair of motors, moving two circles with weights on their rims around, to shift the center of gravity around until it's stable enough to park them on opposite sides?
No. The reaction wheels are generating torque to change the orientation of the cube, not just shifting its center of gravity.
I think that's a little different -- it's pumping liquid around to change attitude (i.e. to point the satellite in a different direction), not to affect its rotational velocity. To get a sustained rotation, you'd have to keep pumping the liquid around continuously, which isn't terribly practical.
Neat idea, though! I wonder if it's being used anywhere, or if reaction wheels won out.
My wheels are oversized when you just consider the balancing application, but I want to add jump-up functionality later, and the wheels need significant inertia (and also need to run at significant speeds) to accomplish that.
Fun project!
Would it be cheaper (and/or safer) to build a larger one, allowing for larger-but-slower flywheels? Could you make one out of a couple of scrap bicycles?