I've got it! A meaning for "move by will alone" that is entirely logical and fits perfectly with the thematic context of the song.

Till now I've been following Carbo.gravy's suggestion that equated "will" with "selfish desire", but the problem here is that actions flowing from unselfish desires are equally an expression of a person's will.
The terms "will" and "volition" have been more or less eliminated from modern philosophy and psychology, but the "will" was initially thought to be that part of the mind/brain that directed a persons actions, based on their desires and beliefs. So a person's will is whatever they want to do, selfish or not.

My problem with "move by will alone" was that I couldn't see what to contrast it with. Obviously we are moved by our "will" if our "will" is that part of us which drives our actions. What else could move us?
That's when it clicked for me. The "will" is what internally drives our actions, but our actions can also be directed by external factors - the nature of our external environment can limit the expression of our internal will.

So "move by will alone" is saying that we can't blame our poor moral choices on these external factors. They are irrelevant. The world presents us with infinite possibilities for moral progression and development so our pathetic failure reflects solely upon our own internal nature, and cannot be blamed on the hostile or impersonal nature of the universe in which we find ourselves.

"Move by will alone" - We can go wherever our will takes us, and yet this is what we choose...