Very good paper. However, it doesn't overcome the problem of superluminal travel. Rather, one of the problems. There are other remaining fundamental physical issues related to FTL, including the need for superluminal matter, causality violation, the impossibility of accelerating past the speed of light and and a few more. Subluminal warps, instead, can be fully consistent with physics.
I believe spherically symmetric bubbles in subluminal regime are more interesting than any warp drive solutions suggested so far. Firstly, they do not require negative energy. Secondly, the passengers in such bubbles age less by the time they reach any destination compared to other warp drives or conventional rockets. Given that exceeding the speed of light is fundamentally prohibited by physics, I would say that spherically symmetric warp drives are the most interesting warp drive constructions we got so far.
In principle, yes, for sure, we could detect it. For example, it would still generate gravity and be uniquely identifiable this way. But then, superluminal matter breaks causality, allows sending signals back in time and, to the best of our knowledge, is unphysical.