[Zigûr]

In "A Postmodern Medievalist" in Tolkien's Modern Middle Ages Verlyn Flieger makes a similar argument to this, so you're definitely not alone in observing the similarities.

Obviously, as you've said, Tolkien could not be called a postmodernist in any serious or formal sense but he (and indeed many other authors before him) took approaches which would later be formalised, codified and (post)modernised by the postmodern movement; consider all the authors who are called "postmodern before postmodernism" even hundreds of years in advance, like Cervantes, Laurence Stern etc. Flieger goes as far back as the Beowful poet as an author who used techniques which might be called postmodern were they to have appeared in, say, 1960s or 1970s literature.

Personally as an enthusiast of both Tolkien and postmodern literature (and I think it is entirely possible to enjoy both) I appreciate seeing the connections. But postmodernism I think, somewhat ironically, has never been as original as its definition suggests. But I still enjoyed Gravity's Rainbow.