[JumpCrisscross]

> would be completely correct and not misleading to say "the springs on the bowling ball accelerated the marble to 2v"

I suppose this is where I disagree. The springs transferred momentum. Your throw (and the resulting motion of the bowling ball) did the work. (Tyres don't accelerate a car, its engine does.)

You could slingshot around a moving body magnetically, the fundamental principles remain the same. The effect of a gravity assist comes from the motion of the body, not gravity per se.

[jessriedel]

“Work done” is the integral of a force.

https://en.wikipedia.org/wiki/Work_(physics)