How is Sibelius anything like the LOTR soundtrack?!
Well, I think if you view the sound track as a whole, you might could make a case for Sibelius, some of the tone poems, maybe Kullervo, possibly the 4th symphony. Maybe.
My 2 fav. tracks are Concerning Hobbits and Many meetings
However, I went back and listened to the two tracks you mentioned. I can see how the, kinda, how the Allegri, might relate, though that's out range of what I listen to (not so strict, but I don't listen to much written before about 1800). So give me an idea if I'm on the right track with what you're looking for. Meeting with the Hobbits made me think of Malcolm Arnold's Scottish dances, particularly the 3rd movement. I'm including the 2nd, well because it's my favorite. I know you should do this, but if you want a visual for it, imagine a Scottish pub, people drinking and dancing, then the bassoon has obviously had a bit too much, and comes lurching in with the theme at half the speed, stumbling about, but having a great time.
3rd Movement:
2nd Movement with apologies, I couldn't find a version I came close to liking. This dude takes it faster than I like and the sound quality totally sucks:
I'm also kinda of thinking Vaughan Williams, Bax, Debussy, Rangstrom all might have some pieces you might like. But I'll need to go back and listen and think some more.
Completely aside, but if you haven't heard the soundtrack from Mists of Avalon, you might give it a shot. Not classical, but you might enjoy it.