Is motion like the following?

[Angrboda]

Is it possible to conceive of a third option vis-à-vis motion?

I think "conceive" is the magic word.  In an idealistic reality, in which all objects are symbolic representations of underlying principles, then movement is really a change in the interaction of principle over time. 

Imagine a car seen in a dream.  Clearly, it is not moving under its own volition, since it is only an idea.  However, is my mind moving it?  I'd argue that the motion is itself only an idea, and that in fact the car is not moving, but rather that the mind is applying the idea of motion to the idea of the car.

So I'd suggest this third option: that reality is idealistic, and that motion is therefore a representation of ideas rather than a property of an object-- self-possessed OR imbued by any second object.  Or, in short, motion is illusory.

This works whether reality is idealistic, or the reality is that we are brains isolated from our percepts.

Btw, self-movement may be constrained by geometry, and thus not random.