How does time "add up" for observers outside of and travelers inside of a Krasnikov tube?
I think one of the most important things you missed in this article is the bit where they say the energy requirements are &quot;unphysical&quot;.  This is no different from saying it's impossible from our point of view.
A couple of quotes from the article :

Here as well, it was found that the wall of the “warp bubble” surrounding a spaceship must be unphysically thin compared to the bubble radius
Estimates of the total negative energy required to construct Krasnikov tubes of even modest dimensions were shown to be unphysically large.  Similar difficulties have been recently shown to plague warp bubbles and wormholes.  The Krasnikov tube suffers from some of the same drawbacks as these other pro
posed methods of faster-than-light travel, and is hence also a very unlikely
possibility.

The model you're discussing is really best thought of as a mathematical exploration, rather than a practical proposal of any kind.  I would suggest the authors are disproving the viability of Krasnikov tubes rather than anything else.  What was done was to try and fix problems with the previous model, but in doing so the authors ( to their credit ) show that they cannot bypass the fundamental problems making such a system unrealisable in practice.