In my humble opinion I think that LOTR came together as a story but was influenced by what Tolkein knew. He was a very learned man in many areas which he would have drawn on as well as being deeply religious (did he not convert to Catholicism?). You need to get your inspiration from somewhere! I think I read somewhere that the idea for 9 rings and one ring to rule them was a Nordic myth.
I also think that perhaps his experiences in WWI might be responsible for the darkness of the "baddies" in the book. They are the stuff of nightmares. In fact although they scared me in the book, when I saw the Return of the King on the big screen certains scenes scared the living daylights out of me in particular Shelob and the massed army in front of Minas Tirith. I am a bit of a woos.
So I am sure that there is a lot of Christianity within the book but I am not sure how deliberate it was. A lot of writers tend to work out their unconcious mind on the page as much as their concious.
Regarding Eye of the World - I have read them all too and I am now waiting for book 11 to come out. If you like books like that then try David Eddings (I love all of his pretty much - the girls are great!) and the Riftwar Saga by Raymond E. Feist and The Mistress of the Empire series by Raymond E. Feist and Janny Wurts. I been reading all of this stuff since I was a teenager and have never really grown out of it:-)