> powering from the outside with the magnetic field of earth
nah quite certain it's just the presence of the electric field from the magnetron source screwing up all their readings. Once you start messing around with >100W magnetron sources the presence of electric fields will show a voltage reading on just about any voltmeter or any sort of voltage measurement device. You need to spend considerable effort to shield all these potential false signal sources.
If you want a simple example, by pass the interlock on a microwave oven and turn it on while you have someone observe a multimeter set to DC volts from across the room. Quite certain they'll get a non-zero reading, even with no electrical leads connected. Just imagine trying to do this while splitting hairs over milli or micro newtons of thrust with an asymmetric microwave oven.
Years ago while working on my bachelor's degree I was messing around with wireless power transmission experiments with a bunch of employed engineers who had not a fucking clue what they were doing. We wasted countless hours taking measurements of supposed RF-to-DC conversion while all we were observing was the electric field strength increasing around us. It took me on my own reverting to the basics of the entire subject and repeating experiment work from William C. Brown's papers to demonstrate to them how to make it actually work right. The whole experience was extremely frustrating while immensely eye opening - a lot of additional letters after a person's name means almost nothing to me now.
Trying to do real science with a bunch of cargo cult true believers is a fool's errand.