Okay, this thread has lain dormant for quite awhile, but I wanted to offer some input.
People noted early in this thread that Tolkien was an academic, a Philology professor. But he wasn't merely a Philology professor. He was a significant Philologist. I remember having to learn assorted "Tolkien laws" when I took a Philology class during grad school. In his academic life, Tolkien studied languages and devised theories to explain his discoveries.
For a hobby, he was not initially a writer. He was a language geek. The writing came later. In fact, he didn't set out to write LotR or The Hobbit and then invent languages to inhabit the stories. He first invented the Elven languages. Then he needed a world where those languages could live, so he invented one. Then he needed stories to inhabit that world. So he wrote them. I think it was his friendship with C.S. Lewis and his meetings with the Inklings that encouraged him to keep working on those stories.
Regardless of whatever cognitive processes we can identify in quotes from Tolkien's fiction, his creative process does not appear to have been a very INFP one. It was grounded in geek stuff.
In my opinion, just from looking at his academic contributions and his creative process, Tolkien = INTP.