Is this solution for interstellar travel viable? I have in mind a way to enable FTL travel. Is this way viable?
In the paper:
"Weighing the vacuum with the Archimedes experiment"
we can see the dependency of the gravitational repulsion exerted by Casimir Vacuum on the energy between the plates.
The force goes as E / c^2.
In the papers:
"Casimir effect with quantized charged spinor matter in background magnetic field"
we can observe that negative energy between the plates can be arbitrarily low if a B field sufficiently strong is provided.
Moreover when the B field diverges the total energy (field energy + Casimir vacuum energy) goes to minus infinite. (see equations 85, 106, 107 for the Casimir vacuum energy)
So this implies that, if a B field sufficiently strong is provided, we can have an arbitrarily strong repulsive gravitational force:
it is exactly what we need in order to make FTL travel possible.
To understand why, read the following:
fact is that, when negative mass is involved, the Shapiro effect changes sign so, instead of a Shapiro delay, you'll have a Shapiro 'early arrival'.
So, in presence of a negative gravitational mass, light (and ultra relativistic particles or spaceships) cover the distance between A and B in a time shorter than d(A,B)/c0.
Where d(. , .) is the ordinary euclidean distance.
For the same reason, in presence of a positive gravitational mass, light (and ultra relativistic particles) cover the distance between A and B in a time higher than d(A,B)/c0.
The aforementioned idea is not new but was presented in
"Microlensing by natural wormholes: Theory and simulations"
 A: The Casimir effect :

The typical example is of the two uncharged conductive plates in a vacuum, placed a few nanometers apart. In a classical description, the lack of an external field means that there is no field between the plates, and no force would be measured between them. When this field is instead studied using the quantum electrodynamic vacuum, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force – either an attraction or a repulsion depending on the specific arrangement of the two plates. Although the Casimir effect can be expressed in terms of virtual particles interacting with the objects, it is best described and more easily calculated in terms of the zero-point energy of a quantized field in the intervening space between the objects. This force has been measured and is a striking example of an effect captured formally by second quantization

Italics and bold mine, for emphasis. The whole effect exists and  depends on the boundaries a few nanometers apart, and nanometers are not compatible with space travel.
Now the link you give about wormholes is a different story that depends completely on negative mass. It is possible to speculate with correct mathematical functions  of General Relativity, and if ever exotic matter with negative mass is discovered maybe it can be used for space travel , bridging distances and seemingly  going faster than light in the  four dimensions of relativity. I do not think that the Casimir effect has been found for dimensions larger than nanometers.
A: I'm not very well informed on this but I see some serious problems with it.
First, the Casimir force is just a loop-level QED effect. It isn't different in nature from any other loop-level effect. I suppose that doesn't prove that it isn't associated with a negative vacuum energy density, but it does take away what seems to be the primary reason that people associate it with negative energy.
Second, if you weigh a system in two configurations with different potential energies, the configuration with the lower potential energy will be lighter because potential energy gravitates. If there is an attractive force between parallel plates then the system will be lighter when the plates are closer together. This says nothing more or less than that the force is attractive. You can write the force as a term due to an invariant mass plus a term due to the potential energy, and if you take the second term to be zero at the larger separation, then it will be an upward "antigravity" term at the smaller separation. But that's just a perturbative expansion. It doesn't prove that nature is using the same zero point as you or that $T^{00}<0$ at any point in spacetime.
Third, your second paper says that their generalized Casimir force is repulsive at high $B$, so the associated potential energy must go to $+\infty$, not $-\infty$, in their approximation.
