I can't help but wonder if Jamie and Adam might have missed an element of the swinging cage "myth." I don't recall the scene from the movie but it seems to me to get the cage to really move
you have to apply more force in the direction you want to go than in the direction opposite you want to go. I'm thinking about this in a F=mass * acceleration sort of way.
Follow with me. The gang runs from one end of the sphere to the other as "best" as they can at a certain rate and all of their collective mass hits the far end which would give a touch of forward momentum. They then move back to the other end of the sphere and begin a gain. I'm thinking by moving back to the other end of the sphere the same way they ran in the direction of desired travel they cancel out the energy they just built up.
I think of when you use a playground swing, if you want to move-forward you kick your legs forward, shifting your weight and then let gravity pull them back to a resting position. (This, of course, is after you've started swinging to begin with by backing up while sitting in the swing.)
So I sort of wonder if there wasn't a way they could've gotten more of swing by being more aggressive in the run-up and let gravity do it's job or just return to the other end in a more gentle way?
But, no matter what, I suspect it wouldn't be possible to get as much swing as they needed without any outside help. The "myth" proved to be a bit more interesting that I was thinking it'd be (and this was a rare case of Jamie/Adam getting the "movie myth, while the Jr. Mythbusters do the more complicated one.)
The pulse-jet drum thing was interesting to see them test and I sort of wonder if more design testing and such could've produced better results? Like their initial "full-scale" design had a very long exhaust port which I suspect soaked up a lot of the energy they were making with the interior explosion. I think a shorter nozzle before going with shorter and narrower.
I agree it seems like "cheating" that they went with a professional to re-tool their design rather than just doing it themselves in the most insane way they could think of but the cart the professional had made was pretty cool.