If that orbital transfer took a long time, someone would argue it's interacting with the Earth's magnetic field.
The only real absolutely unambiguous test I can think of -- other than finding a way to massively boost the effect to the point of undeniability -- would be to launch something at Earth-Moon escape velocity and then see if it can continue to accelerate as long as it's got solar power to do so. For a small test rig this could be done with a small SRB booster from the ISS.
... though on second thought ... I wonder what would happen if you put one of these on a centrifuge? It should spin faster, and faster, and faster... or not. :)
If the effect is too small to overcome friction you could do an experimental / control setup with two centrifuges, one with this device + a normal motor and one with only a normal motor and a ballast of equal mass to the device. Then swap which centrifuge has the device. Repeat many times. The one with the device should consistently accelerate more.
The heat problem sounds like they need to be using superconductors or some means of high-efficiency cooling. I'd look into Peltier effect cooling built into the device or something if superconductivity isn't an option.