As another person commented, you're one tough cookie to expect Arwen to take Aragorn's and her own deaths with a positive attitude, considering that her experience as a mortal woman was a tiny fraction of her life and she was not granted the vision that Aragorn evidently had about the eternal continuation of the soul. That is how I understand the doom/gift of men: doomed to die but gifted with an immortal soul which death cannot touch. From Arwen's experience as an elf before becoming mortal (well, half-elf), elven death is true death because while the elves are immortal in body if unharmed by accident or battle, when they die that's it. That's why they have to journey physically back to the Blessed Realm. At least, that's how I've always understood the back story of Middle Earth.
Personally, I think you're reading too much into a few phrases and putting your own spin on it. This is one of those "Balrogs have wings / not" arguments that I don't think we're going to settle, but I admit your take is interesting and thought-provoking.
For me, Lord of the Rings has a "happy" ending considering that death will take all mortal men (and women) and the elder races are doomed to fade away (or, worse, become evil). That much was known and set before the story really began, and there is nothing that the characters could have done to change those two things. The essence of tragedy is that the characters make the wrong choices and don't do the best they can with the opportunities at hand. In this case, the characters make the right choices, so I can't call it a tragedy.
Except that Arwen no longer has a choice:
"Nay, dear lord," she said, "that choice is long over. There is now no ship that would bear me hence, and I must indeed abide the Doom of Men, whether I will or nill: the loss and the silence.