It's even more accurate, and a far simpler explanation of Tuvix's words, to say that Tuvok and Neelix had their personalities, memories, etc. combined into Tuvix which created a new being (Tuvix) and killed the original two (Tuvok and Neelix). When Tuvix says that Tuvok and Neelix live within him, he's speaking as metaphorically as anybody else who says their parents live on through them. And when Tuvix was murdered, splitting him into Tuvok and Neelix, they weren't the same beings but exact duplicates - much as O'Brien on DS9 or Harry Kim on Voyager.
I'll leave the religious discussion of bringing the dead back to life go for now.
I couldn't care less whether Tuvix was speaking metaphorically or not. The FACT was that Tuvok and Neelix could be brought back to life; therefore, they were not "dead." Tuvix's personal interpretation of the situation is irrelevant, "poetic license" or not.
What?

It's extremely important, in fact critical, to establish whether Tuvix was speaking metaphorically or literally.
After all, if Tuvok and Neelix were literally alive within him and wanted to be re-separated, then a strong case can be made that Tuvix is a kidnapper/hostage-taker. In which case, Tuvix becomes a parasitical being and
Voyager's crew should have tried to find a way to separate the Tuvix being from Tuvok and Neelix while preserving all three.
If on the other hand (as I maintain) Tuvix is speaking metaphorically/poetically and there are no separate/trapped Tuvok/Neelix consciousnesses, then they have ceased to exist and Tuvix is the only being present - and thus, the only one with a voice.
In our universe, the dead cannot be revived. The Star Trek universe, however is a place where the dead can be brought back to life; thus, reviving Tuvok and Neelix doesn't indicate that they weren't, in fact, dead. See for example Voyager's own "
Mortal Coil." "
Hide and Q" (and perhaps "
Encounter at Farpoint") also establishes that the Q have the power to restore the dead to life.
Can you prove that Tuvok and Neelix were "new?" Can you define what constututes a "new being" as opposed to an "old being" and prove that your interpretation is the correct one? The nature of consciousness has been an ongoing discussion among scientists and philosophers for ages, and, to the best of my knowledge, the precise nature and value of "consciousness" has not yet been resolved.
I don't believe Tuvok and Neelix were "new" in any practical sense, but they stopped existing, were non-existent for a period of time, and were brought back to existence. I suggest they were exact duplicates of the originals, and equally valid and deserving of life and "replaced" the originals. Just as Harry Kim is not the original Harry Kim, but an equally valid and deserving version. Just as Tuvix was equally valid and deserving of life.
If Tuvok and Neelix had the same memories, personalities, and genetics as before they were "combined," then why aren't they still Tuvok and Neelix after they were reconstituted?
There's no "still" about it. Remember, this is a universe in which Tasha Yar came from the future, was captured, raped, and eventually murdered by Romulans, and was later born, grew up, served the Federation, and was killed by Armus. Was Tasha Yar post-
Yesterday's Enterprise the same person as the Tasha Yar who was later killed by Armus? No, but she was still Tasha Yar.
Same thing with Miles O'Brien post-
Visionary, though much less dramatic.
If you really wanted to follow that thought through, you could say that a person isn't the "same being" as before they go to sleep after they wake up. You're not even the "same" person from one moment to next moment. It's called the "Bundle Theory of Consciousness," but it does not provide a practical justification for eliminating a person.
You're right. A transporter accident, however, does provide a practical justification for eliminating a person, especially when the restoration involves the unwilling death of another sentient being.
Are you the same person you were five minutes ago? Are you not as valuable now as the person who was alive five minutes ago? If I kicked you in the face, does it not matter because you'll be a "different" person in five minutes?
My existing, however (or re-existing), does not depend on the death of another person who is unwilling to die.