I think you are focusing on the wrong thing.
The eucatastrophe was that Earendil won through to the West, the Valar came and defeated Morgoth, Morgoth's body was executed and his spirit cast out. On the face of it the odds of this happening were at least as bad as Frodo making it to Mount Doom and casting the Ring into the Fire.
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The end of the Sil does not possess that hope, in my opinion. Morgoth is banished to the Void (not even destroyed!) and his hate and other seeds of evil live on.
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Neither was evil destroyed at the end of LOTR. Sauron was overthrown, but other seeds of evil lived on.
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Maybe part of the reason for the lack of eucatastrophe (aside from the plot itself) is the style in which it is written. In many places, it is much more 'documented' than LotR is.
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I think this has a lot to do with it. The description of Earendil's journey could (generously) be called detached. We don't know what they went through. If the rendering of the story had been more personal the effect would have been quite different.
[EDIT] Also note that Earendil and Elwing paid a price for the accomplishment of their quest, similar to Frodo.