I take your point, but it's risky. There are fragments of Middle Earth history of the period referenced in the published canon -- Gollum's wanderings; Aragorn tracking Gollum; the White Council driving Sauron from Dol Guldur; Aragorn's romance with Arwen; the dwarves' war with the orcs -- but nothing developed as a story by Tolkein.
Pretty risky territory. Strikes me as similar to that Gone With The Wind sequel a few years back.