To save Tuvix was to murder Tuvok and Neelix.

They could've attempted to recreate the Riker accident. Copy the datastream before it's split. Surely there's the technical knowledge to do it.

It's also interesting that at the end of the episode, they never go into Tuvok and Neelix' memories of the whole thing - they don't seem surprised to be in sickbay instead of the transporter room, so they're clearly aware of what happened. They could have at least asked them at that point whether they're happy to be back of if they would like to be merged again - they've shown that it's just a matter of having the orchid in the same transport.

In fact, that they're not confused by the - for them individually - new memories, like Tuvix was when he first came into being, could actually suggest that they were both actively present to some degree inside Tuvix' personality...

Aside from all that, the way they explain the orchid's effect means that it would never have been safe to have Tuvix in a shared transporter stream: the orchid's means of reproduction is basically to merge with another species through the use of a particular enzyme, so it stands to reason that Tuvix is the orchid's offspring and also possesses that enzyme.