Your reasoning is flawed. The argument against the Alcubierre drive cannot stem from special relativity as it would only apply if there were a violation of local causality.
The problem is that using an Alcubierre drive, one could construct closed timelike curves, which are impossible in a 3+1-dimensional, asymptotically flat and singularity-free spacetime where the weak energy condition holds.
Also keep in mind that FTL is less problematic than many physicists think, even in special relativity - see eg 'Tachyon Kinematics and Causality: A Systematic Thorough Analysis of the Tachyon Causal Paradoxes' by Recami.
My reasoning is not flawed. And the paper you pointed me on re tachyons, specifically states that we cannot use tachyons to transmit information via them.
I never stated that nothing can travel faster than light. Only that WE cannot travel faster than light, nor can we transmit information faster than light, without violating causality.
On the other hand, maybe we can violate causality.
The problem is that using an Alcubierre drive, one could construct closed timelike curves, which are impossible in a 3+1-dimensional, asymptotically flat and singularity-free spacetime where the weak energy condition holds.
Also keep in mind that FTL is less problematic than many physicists think, even in special relativity - see eg 'Tachyon Kinematics and Causality: A Systematic Thorough Analysis of the Tachyon Causal Paradoxes' by Recami.