The "uninterrupted stream of consciousness" argument is incredibly flawed. How can such a thing exist when your brain is disassembled and converted to energy at the subatomic level?
How can such a thing exist? Very well, apparently.
How do Heisenberg compensators work? How does warp drive work? Replicators?
is full of implausible technologies, but they are part of the conceits of the ST Universe. One of those conceits, firmly established in the canon, is that a person who is beamed by a properly-functioning transporter, has complete continuity of consciousness.
Tuvok and Neelix, in this episode, do not. They are dead; the Tuvok and Neelix who are created at the end of the episode are copies, not the originals.
And, yes, I'm inclined to make similar arguments about the William Riker/Thomas Riker incident, and even the "Enemy Within" scenario. I think the original William T. Riker died in that accident established in "Second Chances," and that the two Rikers created by that are copies, not the original -- that, in other words, the William T. Riker born in Alaska should have been declared legally dead and his copies issued their own separate birth certificates backdated to the time of the transporter accident, given their own Federation Social Security Numbers (or whatever the UFP uses), etc. Same with the Evil!Kirk and Good!Kirk, and then with the resulting Reintegrated!Kirk. Etc.