You talk about wanting to find a solution, so I'd like to share where I think one might be found. Not that I've found it, I just think I know where to look.

The problem with books is that we live in a partially post-scarcity society. Star Trek envisioned post-scarcity everything, but we live in a partially post-scarcity society: Food, pure metals, clean water etc. are all still scarce, but anything that can be digitized is not. Books can be digitized, so they are subject to post-scarcity economics, but most of the author's needs are subject to scarcity economics.

What bridges the these two economies, and where I believe the answer can be found, is in attention. Attention is scarce, but it is also necessary to consume anything in the post-scarcity economy. It exists in both worlds somehow, and I therefore believe it's closely related to the problem of how an author can get paid.