Okay: time to cheat. From my attempts at making a square riddle generator, I still have a list of all the articles on the Encyclopedia of Arda. Attacking that with what we know:
-'Muck+Sin' is the easiest to eliminate. U,K, and S only appear together in 7 entries, and none of them come close. (The only Hobbitish one is 'Bucklanders'; I guess they don't have an article called 'Brandybucks', but there's no B anyway.)
-'Mud+Sin' is almost as easy, because D isn't very common either. It does pop up the awesomely-named Dudo Baggins, but other than that it's mostly various phrases.
-'Mire' looks like a stretch for 'filth', so I'll skip it for now; it's also not very easy to find a concise search string for. (Yes, I could just look for anything that contains all the letters, but I'd rather not.)
-'Grime+Sin' has G, R, and S; that gives a lot of hits for 'great', but does finally take me down to:
ISENGRIM Took, the name of three Thains of the Shire. The first is of unknown date, the second presided over the building of the Great Smials (and the adjustment of the calendar, and the first growing of pipe-weed...), and the third a short-reigning son of the Old Took. The name comes from a mythical wolf, but sadly there's no attested harsh winters that could lead to a delightful Hobbit epic about Thain Isengrim I and the Wolf.
hS
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