So much this. And it can be done without any additional information from the works not covered by the existing movie rights - after all, most of the information about the Third Age exists pretty much only (at least in a finished form) in the Appendices to LotR.

Story of the fall of Arnor/Arthedain, including defeating the Witch King? Story of the Kin-strife in Gondor? Fighting the Corsairs of Umbar?

In fact, a story I would pay gold to see, and which can easily be tied into the films, is the one about the exploits of young Aragorn - as a Ranger in the North, then in the courts of Gondor and Rohan, and in the lands of Rhun and Harad. Even the title writes itself: "Where the Stars are Strange"...