[littlemanpoet]

Is there a specific kind of Middle-earth improvement that I cannot gain from any other book, or is it merely one pathway among many to the same place?

Eucatastrophe. Perhaps it exists in other books, but I haven't been affected by this in other books as I have in LotR. This is one way in which I became better than I was. I had given way to despair (for various reasons that are not to the point), and partly through the book, and partly through a certain BD discussion thread, I was reminded of the hope in LotR, that some kind of good can come out of seemingly insurmountable evil. Hope has been a re-starting point for a personal renaissance of the spirit.

Are those of us who are made better by the book, or who better ourselves in response to the book, better in the same way?

In part yes, in part no. The former is passive, something that happens to us, whereas the latter is something we do ourselves. That has to account for some difference. Don't you think that being made better (a realization), must precede choosing to be better (conscious action)?

Is there a bit of Tolkien in all of us, or are we just rising to a challenge presented by the book in our own unique ways?

There's a level at which, obviously, there's a bit of Tolkien in all of us, in that we share humanity; but I think you're shooting for something more specific. There seems to me to be a lot of middle ground between your either and or in this question. Might you clarify it?